De Broglie's hypothesis. Hvili de Broglie.
As it was said earlier, light (and flame reversal) is of a secondary nature: in some phenomena (interference, diffraction, etc.) light occurs as a contortion, in other phenomena with no less reversibility - as a part nki. This is what prompted de Broglie (b. 1923) to derive the idea from the fact that material parts are subject to the influence of the authorities, then. expand such corpuscular-whili dualism into parts with a mass of calm, subsumed from zero.
Since such a lot of sickness is associated with it, you will notice that it is widening with direct fluidity υ parts. De Broglie did not discover anything about the nature of this story. Let us not yet understand its nature, although we would like to point out that these things are not electromagnetic. The stench seems to be of a specific nature, which has no analogue in classical physics.
Well, de Broglie formulated a hypothesis that the impulse is related to p=ћω/c The fact that photons exist is universal in nature, so that the particles can be given a twist, the end of which
This formula was given a name de Broglie's formula, and λ – De Broglie's birthday particles with momentum R.
De Broglie also allowed a bunch of particles to fall onto the valley and interfere with them.
Other, independent from formula (3.13.1) relationships are connections between energy E particles with a frequency of ω de Broglie's wave:
Basically, energy E determined first with accuracy until a sufficiently constant value has been added (on the basis of Δ E), however, frequency is a fundamentally unguarded quantity (as opposed to the de-Broglie dovetail).
With frequency and number k two speeds are connected - phase υ f that group u:
(3.13.3)
Multiplying the number and sign of both expressions by ћ from the equations (3.13.1) and (3.13.2), we reject it, having taken a look at the non-relativistic appearance, then. respectfully E = p 2 /2m(kinetic energy):
(3.13.4)
It can be seen that the group fluidity is similar to the particle fluidity, which is the value that is fundamentally guarded against change υ f - through ambiguity E.
From the first formula (3.13.4) it follows that the phase fluidity of the de-Broglie horns
(3.13.5)
to lie below the frequency ω, which means the de-Broglie quills loom dispersion in the vacuum. It will be shown below that it is clear to the current physical interpretation that the phase fluidity of De Broglie’s forks has a more symbolic meaning, as long as this interpretation brings them to the principle of non-sterility any values. However, what has been said is clear and immediately E in (3.13.5) it is stated, as was said, with accuracy to a fairly constant degree.
The discovery of the fact that (3.13.4) the group fluidity of de Broglie’s fortifications is the modern fluidity of parts, played an important role in the development of the fundamental principles of quantum physics, and then in the physical interpretation these de-Broglie hvils. Initially, an attempt was made to look at the particles as small packages of even small length and in this way to create the paradox of the duality of the powers of the particles. However, such an interpretation appeared in Milk’s opinion, since all warehouse packages of harmonious fluids are expanding with different phase fluids. Due to the evidence of great dispersion, the powerful de-Broglie khvils say in a vacuum, the khvilovsky package is “spilling”. For parts with a mass of the order of the electron mass, the package is poured practically into a mixture, as well as for stable solutions.
In such a manner, giving a piece of food in front of a package of leather turned out to be impossible. The problem of the duality of powers of the particles required a different approach to its solution.
Let's return to de Broglie's hypothesis. It is clear that in some phenomena the power of the particles may be revealed, as the stink of power actually appears. We know that regardless physical nature hvil - this is interference and diffraction. To be careful in them is the essence of the disease. In all cases, the de Broglie's dowry is determined by the formula (3.13.1). Let us carry out some assessments with her help.
We must first understand that the de Broglie hypothesis does not fit the concepts of macroscopic physics. Let's take it as a macroscopic object, for example, a powder, respectfully, what is it? m= 1 mg liquidity V= 1 µm/s. This is a true de-Broglie's birthday
(3.13.6)
That is, in such a small macroscopic object, like a powder of de Broglie’s dovegne, the truth appears to be significantly smaller than the size of the object itself. In such minds, none of the powerful powers of the world can manifest themselves in the minds of accessible dimensions.
The other one on the right, for example, has an electron with kinetic energy K and with impulse . Yogo de Broglie's birthday
(3.13.7)
de K It is expressed in electron volts (eV). At K= 150 eV de-Broglie dovzhina khvilі electron dovnyuє zgіdno (3.13.7) λ = 0.1 nm. A stationary crystalline lattice is of the same order of magnitude. Therefore, similar to the case of X-ray measurements, the crystalline structure can be a suitable means for eliminating the diffraction of de-Broglie electrons. However, de Broglie’s hypothesis was so unrealistic that it did not lend itself to experimental revision for a long time.
Experimentally, de Broglie's hypothesis was confirmed by the research of Devson and Germer (1927). The idea of these traces was in the offing. Since a beam of electrons has powerful effects, it is possible to perceive, without knowing the mechanism of their generation, that the generation from the crystal is of the same interferential nature as X-ray changes.
In one series of studies by Devisson and Germer, in order to identify diffraction maxima (such as such), the electron voltages were measured, which accelerate and simultaneously the positions of the detector D(repair of damaged electrons). The final nickel single crystal (cubic system) was polished as shown in Fig. 3.13. How to rotate it around the vertical axis Fig. 3.13.1
The position that indicates the baby, then in what position
The surface is polished and covered with regular rows of atoms, perpendicular to the flat surface (baby plane), standing between them d= 0.215 nm. The detector was moved near the valley surface, changing cut θ. With vugilla θ = 50 0 and prestress stress V= 54B, being careful of a particularly high maximum in Fig. 3.13.2.
This maximum can be considered as a first-order interference maximum from a plane diffraction grating from the designated higher period in accordance with the formula.
This can be seen in Fig. 3.13.3. On this skin, a fatty point on the skin is a projection of a band of atoms, spread out on a straight line, perpendicular to the surface of the skin. Period d may be affected independently, for example, by X-ray diffraction. Fig.3.13.3.
Calculated using the formula (3.13.7) de Broglie's dowzhina for V= 54B is higher than 0.167 nm. The maximum value of the flux, found from formula (3.13.8), is equal to 0.165 nm. The results are so good that the result is consistent with the confirmation of de Broglie's hypothesis.
Other evidence that confirmed de Broglie’s hypothesis was that of Thomson and Tartakovsky . In these studies, a beam of electrons was passed through a polycrystalline foil (using the Debye method using X-ray diffraction). As with the X-ray experiment, a system of diffraction rings was placed on the photographic plate, spread behind the foil. The similarity of both paintings is striking. It is suspected that the system of these rings is generated not by electrons, but by secondary X-ray vibrations, which stems from the fall of electrons on the foil, which easily dissipates when a magician creates the path of scattering electrons no field (bring a permanent magnet). X-ray vibration is pouring in. This re-verification showed that the interference picture was immediately reversed. It is clear that we can rightly be with the electrons.
G. Thomson has carried out research on small electrons (tens of keV), P.S. Tarkovsky - with high-volume electrons (up to 1.7 keV).
To successfully control the diffraction of crystals, it is necessary that the majority of the crystals be leveled between the nodes of the crystal systems. Therefore, in order to prevent diffraction of important particles, it is necessary to add small amounts of particles. Evidence from the diffraction of neutrons and molecules when the crystals were dissolved and also completely confirmed the de-Broglie hypothesis that the crystals were solidified down to important particles.
After all, it has been experimentally proven that the Hvilian power is the universal power of all parts. The stinks are not influenced by any peculiarities of the inner being of this or other parts, but are inspired by their corrupt law to the ruin.
The descriptions have mostly been based on the vicinity of particle beams. This is due to natural nutrition: the power of a bunch of particles or several particles?
To put this in perspective, V. Fabrikant, L. Biberman and N. Sushkin created it in 1949. Find out in which such weak electron beams were stuck that each electron passing through the crystal was clearly one by one, and each electron scattering was recorded by a photographic plate. In this case, it turned out that the electrons were lost in various parts of the photographic plate, absolutely innocent at first glance (Fig. 3.13.4) A). For an hour after a long exposure, a diffraction pattern appeared on the photographic plate (Fig. 3.13.4 b), is absolutely identical to the diffraction pattern from an emergency electron beam. So it was confirmed that the Khvilov authorities will cut down the parts.
In this way, we can deal with micro-objects that move around at the same time as corpuscular ones, and also
them by the authorities. This allows us to speak further
about electronics, ale visnovki, which we will come, toil Fig. 3.13.4.
zagalny place and, however, stagnation down to any parts.
Paradoxical behavior of microparticles.
The experiments reviewed in the previous paragraph show that we are faced with one of the most mysterious paradoxes: what does the firmament “electron” mean?»?
Let's try to ask someone for an explicit experiment similar to Young's discovery of the interference of light (photons) from two slits. After a beam of electrons passes through two slits, a system of maxima and minima is created on the screen, the positions of which can be determined by the formulas of cow optics, just as the skin electron is given a de-Broglie pintle.
The very essence of quantum theory is hidden in the apparent interference between the two chasms, to which special respect is due.
As we are dealing with photons, the paradox (part of it) can be understood by assuming that the photon, through its specificity, splits into two parts (at the gaps), which then interfere.
What about electronics? Even the stench does not spit out - it is installed reliably. An electron can pass through gap 1 or through gap 2 (Fig. 3.13.5). Also, the division on the screen is the sum of divisions 1 and 2 (Fig. 3.13.5 A) - shown as a dotted curve. Fig.13.13.5.
Although the logic in this world is unfounded, such a division does not work. We are aware of a completely different division (Fig. 3.13.5 b).
Is this not an accident of pure logic and healthy intelligence? Everything looks like this, if 100 + 100 = 0 (at point P). In fact, if either gap 1 or gap 2 is open, then say, 100 electrons per second arrive at point P, and if the gap is opened, then so on!
Moreover, if you initially open gap 1, and then step by step open gap 2, increasing its width, then behind a healthy depth the number of electrons that come to point P when pressed may increase in 1 00 to 200. Actually, it’s from 100 to zero.
If you repeat this procedure, registering parts, for example, at point O (div. Fig. 3.13.5 b), the result is no less paradoxical. When gap 2 is opened (with gap 1 open), the number of particles at point O increases not to 200 per second, as a result, but to 400!
Yak From the opening of gap 2, can it be pressed onto the electronics, which, presumably, would pass through gap 1? That is, on the right, so that the skin electron, passing through this gap, “sees” and this gap, correcting its behavior. Or it’s like a pain in the ass to go straight through hurtful gaps (!?). Even otherwise, the interference pattern cannot be understood. The attempt is still to determine which gap the same electron passes through, leading to the formation of an interference pattern, and thus a completely different supply.
What kind of visnovok? A single method of “explanation” of these paradoxical results lies in the creation of mathematical formalism, which is consistent with the results that are rejected and the phenomena are always correctly predicted. Moreover, obviously, this formalism may be internally inconsistent.
And such formalism was created. It is important to place the appearance of the skin particle under the complex psi-function Ψ( r, t). Formally, she has the power of the classical warriors, which is often called hvil function. The behavior of the free one crumbles evenly at the singing straightness of the particles describing the flat de Broglie
There will be more information about this function, physical sense and jealousy, which is reflected in their behavior in space and time, in the next lecture.
Turning to the behavior of electrons during the hour of passage through two slits, we can recognize: the fact that, in principle, it is impossible to supply the power through which the electron can pass(Not a constant interference pattern), crazy about the statements about the trajectory. In this way, the electrons, seemingly burning, cannot be attributed to trajectories..
However, for the sake of singing minds, and if the De-Broglie Dovzhina of microparticles becomes even small and may appear much smaller, for example, between the cracks or atomic dimensions, the concept of the trajectory of a new surge є sense. Let's take a look at this report and formulate it more correctly in the minds of which we can quickly formulate the classical theory.
The principle of insignificance
In classical physics, the final description of the state of a particle is determined by dynamic parameters, such as coordinates, momentum, angular momentum, energy, etc. However, the actual behavior of microparticles shows that the underlying principle is interprecision, for which such changes can be indicated and changed.
A deep analysis of the reasons for the creation of this boundary, as we call it the principle of insignificance, Prov V. Heisenberg (b. 1927). Several relationships that express this principle in specific situations are called with the relationship of insignificances.
The individuality of the authorities of microparticles is manifested in the fact that Not all the important ones come out when the songs die out. There are pairs of quantities that can be calculated exactly at the same time.
The most important are two relationships of insignificances.
First, the accuracy of the one-hour measurement of coordinates and the corresponding projections of the pulse portion are distinguished. For projection, for example, onto the whole X it looks like this:
Another relationship establishes the insignificance of the vanished energy, Δ E, For the given interval of an hour Δ t:
Let us explain the relationship between these two. First, they are solidified because the position of the particles, for example, is along the axis X obviously unimportant Δ x, then at the same moment the projection of the particle’s impulse onto the whole can only be considered unimportant Δ p= ћ/Δ x. Please note that this exchange does not interfere with the one-hour calculation of the coordinates of the particle along one axis and the projection of the impulse - according to other values: xі p y, yі p x and so on can provide more precise values at the same time.
Compatible with other relationships (3.13.11) for vibrating energy with the loss of Δ E an hour is required, no less, less Δ t=ћ /Δ E. The butt can be used to “distribute” the energy levels of water systems (at the same time as the main camp). Therefore, the hour of life is valued at about 10 -8 points in all destroyed systems. The development of equal parts leads to the expansion of spectral lines (natural expansion), which is truly guarded against. This applies even to any unstable system. As every hour of life continues until the order falls apart, then through the end of that hour the energy of the system becomes indispensable, not less, less Δ E≈ ћ/τ.
It is also possible to find pairs of quantities that can be accurately calculated at the same time. Here are two projections to the moment of the impulse. Tom I won’t understand, in which all three and send some kind of two out of three projections to the moment of impulse of small significance.
We will discuss the report and the possibility of communication Δ x·Δ p x ≥ ћ . We have the utmost respect for those who signify the principle between insignificances Δ x ta Δ p x, because of which parts of the country can be characterized classically, then. coordinate x and the projection of the impulse p x. Which is more precise? x, thus with less accuracy, you can install p x, i just like that.
It is worth noting that the relevant sense of the relationship (3.13.10) reflects the fact that in nature there is no objective formation of particles with precisely defined values of both variables, xі p X. At the same time, about those changes, the fragments of death are carried out using additional macroscopic devices, attributing classical changes to parts not in power. The shortcomings of such an approach lead to the emergence of inconsistencies.
Since there was a need to describe the behavior of the particles using cow functions, the relationships of insignificances appear to be a natural phenomenon - as a mathematical inheritance of the theory.
Importantly, the relationship of insignificances (3.13.10) is universal, it is appreciable how it appeared in Russia as a macroscopic body. Let's take a small bag of masa m= 1 mg. It is significant, for example, with the help of a microscope in its position in the abduction Δ x≈ 10 -5 cm (this is equipped with a separate part of the microscope). Therefore, the fluidity of the bag is unimportant Δυ = Δ p/m≈ (ћ /Δ x)/m~ 10-19 cm/s. Such a value is inaccessible to the standard world, and the access to the classical description is completely absent. In other words, for such a small (or macroscopic) bag, the concept of trajectory can be defined with a high level of accuracy.
This is how electrons work in an atom. A rough estimate shows that the insignificance of the fluidity of the electron, which collapses in the Bohr orbit of the water atom, can be equalized with the fluidity itself: Δυ ≈ υ. In this situation, the phenomenon of the electron falling along the classical orbit loses its senses. I started to burst into flames, with the presence of microparticles in even small areas, it is impossible to clearly understand the trajectory.
At the same time, behind the singing minds, the flow of microparticles can be seen classically as a trajectory of the flow. This is the case, for example, during the collapse of charged particles in electromagnetic fields (in electron tubes, accelerators, etc.). These forces can be seen classically, the fragments for them are boundaries, understandings of the relationships of insignificances, even small in alignment with the values themselves (coordinates and impulse).
Evidence from the gap. The relationship of insignificances (3.13.10) manifests itself through any attempt to accurately measure the position or impulse of a microparticle. And we immediately arrive at a “unpretentious” result: clarification of the position of the part leads to an increase in the insignificance of the impulse and in the end. As an illustration of such a situation, let's look at the offensive butt.
Let's try to calculate the coordinate x collapses with momentum p pieces that placed a screen the width of a slit on this path perpendicular to the ridge b(Fig.3.13.6). Before the passage of the part through the gap, its projection to the impulse p x has more precise values: p x = 0. Tse means that Δ p x = 0, but
Coordinate x parts are absolutely unidentified (3.13.10): we cannot say, Fig. 3.13.6.
If you are given a piece of land to pass through the gap.
If a section passes through a chasm, then in the plane of the chasm the coordinate x will be registered as unimportant Δ x ≈ b. In this case, as a result of diffraction with the greatest intensity, the part falls between the 2θ point, where θ is the cut point, which indicates the first diffraction minimum. Vіn is determined by the mind, for any difference in the course of the forks on both edges of the thickness of the λ (not to be found in the hwyl optics):
Due to diffraction, the insignificance of the value is to blame p x - projections to the impulse, the distribution of which
Vrahovoyuchi scho b≈ Δ Xі p= 2π ћ /λ., subtracted from the two front expressions:
which is determined by the order of magnitude (3.13.10).
In this manner, try to determine the coordinate x the particles, in truth, led to the appearance of insignificance Δ p the impulse has parts.
Analysis of many situations related to vimirs shows that vimirs in the quantum field are fundamentally differentiated from classical vimirs. In addition to the rest, quantum physics has a natural inter-precision between worlds. Because of the very nature of quantum objects, they may be subject to some sophisticated adaptations and methods of extinction. Spіvіdnoshenya (3.13.10) establishes one of these inter-connections. The interaction between a microparticle and a macroscopic vibrating device cannot be achieved as quickly as possible. Vibration, for example, of the coordinates of a particle, inevitably leads to a fundamentally indiscriminate and uncontrolled reaction of microparticles, and therefore to insignificance of the given impulse.
Deyaki vysnovka.
The relationship of insignificances (3.13.10) is one of the fundamental provisions of quantum theory. One relationship is enough to eliminate low-important results, for example:
1. A weak camp, in any part of the camp there would be peace.
2. When considering the development of a quantum object, it is necessary in many cases to come to terms with the concept of a classical trajectory.
3. Frequently expends sensory energy E particles (like a quantum object) for potential U and kinetic K. True, persha, tobto. U lie in the coordinates, and the other - in the impulse. These are dynamic changes that are inescapable and of immediate significance.
4.4.1. De Broglie's hypothesis
An important stage in the development of quantum mechanics was the discovery of the power of microparticles. The idea of the Khvilian power was initially formulated as a hypothesis by the French physicist Louis de Broglie.
For many years, physicists have had a theory behind which there is an electromagnetic phenomenon. However, after Planck works ( thermal ventilation), Einstein (photo effect) and others, it became obvious that corpuscular power shines brightly.
To explain the workings of physical phenomena, look at the light as a flow of photon particles. The corpuscular power of the world will not be counteracted, but will be reinforced by its power.
Otje, The photon is an elemental part of the light that holds the power of the Hvilians.
Formula for photon momentum
| . | (4.4.3) |
Following de Broglie, the collapse of a particle, for example, an electron, is similar to the process of the dowzhin λ, which is expressed by formula (4.4.3). These hvili are called Hvilami de Broglie. Also, particles (electrons, neutrons, protons, ions, atoms, molecules) can exhibit diffraction powers.
K. Davisson and L. Germer were the first to understand the diffraction of electrons on nickel single crystals.
What can you figure out: what happens to the surrounding particles, how are maxima and minimums created during the diffraction of surrounding particles?
Research on the diffraction of even low-intensity electron beams, that is, of adjacent particles, showed that in this case the electron does not “spread out” along different directions, but moves like a whole piece. However, the probability of electron emission across adjacent directions as a result of interaction with the diffraction object differs. The most likely occurrence of electrons is in those areas that correspond to diffraction maxima, and the least likely occurrence is in the area of minimum values. Well, the Khvil authorities are attached to the collective of electrons, and to the skin electron.
4.4.2. Hwil's function and physical sense
So, since a microparticle is subject to a mechanical process, which is indicative of its direction, then the state of particles in quantum mechanics is described by a mechanical function, which lies at the coordinates and time: .
Since the force field that acts on a particle is stationary, so as not to lie in time, then the ψ-function can be represented in the form of two partners, one of which lies in time, and the other type of coordinates:
The result is a physical change in the spine function:
4.4.3. The relationship of insignificances
One of the important provisions of quantum mechanics is the relationship of insignificances, proposed by W. Heisenberg.
Let the position and momentum of the particle suddenly vibrate, with inaccuracy in the values of the abscise and the projection of the impulse onto the entire abscise of the same level: Δx and Δр x.
In classical physics, there are no common boundaries that can be protected with any level of accuracy to simultaneously measure one or another value, so that Δx→0 and Δрx→0.
Quantum mechanics has a fundamentally different position: Δx and Δр x, which corresponds to the one-hour value of x and р x related to location
Formulas (4.4.8), (4.4.9) are called with the relationship of insignificances.
This can be explained using one model experiment.
When the phenomenon of diffraction was introduced, it was believed that changing the width of the gap during diffraction would lead to an increase in the width of the central maximum. A similar phenomenon will occur in the diffraction of electrons by a gap in a model light. A change in the width of the gap means a change in x (Fig. 4.4.1), which leads to a greater “smearing” of the electron beam, which leads to greater insignificance of the impulse and fluidity of the particles.
Small 4.4.1. Explanation of the insignificance.
Spіvіdnosheniya insignificance can be filed in the form
| , | (4.4.10) |
where ΔE is the insignificance of the energy of the system; Δt - the period of time during which it sleeps. Comparison (4.4.10) means that less than an hour of awakening of any system, the value of its energy is no longer known. Energy levels E1, E2, etc. draw the width of the deck (Fig. 4.4.2)), so that it remains in place at the time of system restart at the station, which is indicative of this level.
Small 4.4.2. Energy levels E1, E2, etc. draw the width.
The “proliferation” of the levels leads to the insignificance of the energy ΔE of the propagated photon of the same frequency Δν when the system transitions from one energy level to another:
,
de m-masa particles; ; E and E n - full potential energy (potential energy is determined by the force field in which the part is located, and for a stationary phase it does not lie for an hour)
If a particle moves along any given line, for example, along the OX axis (one-dimensional fall), then the Schrödinger equation disappears and begins to appear
 | (4.4.13) |
One of the simplest applications of the Schrödinger equation is the problem of collapsing particles in a one-dimensional potential well.
4.4.5. Zastosuvannya Schrödinger's equation to the atom of water. Quantum numbers
The description of the conditions of atoms and molecules with the help of Schrödinger’s equation is sufficient for complex tasks. It is simplest for one electron located in the field of the nucleus. Such systems correspond to water atoms and water ions (single ionization of a helium atom, single-ionization of a helium atom, etc.). However, in this case, the highest level of information is complicated, which is surrounded by a very clear nutritional plan.
Nasam -ide at Rivnyann Shredinger (4.4.12) Slid Pіdstaviti Potzіin Energius, yak for the two mutual boobs cigarette - E (Electron) I ze (nucleus), Sho is to be found at Vidstani R at Vakuumi, Viralzhatu is so rustic:
This is determined by Schrödinger's equation and is completely compatible with the similar formula of Bohr's theory (4.2.30)
Figure 4.4.3 shows the possible values of the total energy of a water atom (E1, E2, E3, etc.) and the graph of the potential energy En as a result of the difference between the electron and the nucleus. As the head quantum number n increases, r increases (div. 4.2.26), and the potential energy increases again (4.4.15) from zero. Kinetic energy is also equal to zero. The shaded area (E>0) indicates the state of a free electron.
Small 4.4.3. Shown is the possible value of the constant energy of a water atom
This is a graph of the potential energy content between the electron and the nucleus.
Another quantum number - orbital l, given n, the values 0, 1, 2, ...., n-1 can be generated. This number characterizes the orbital angular momentum L i of the electron about the nucleus:
Quarter quantum number - spin m s. There can be up to two values (±1/2) and characterizes the possible values of the electron spin projection:
| .(4.4.18) |
The state of the electron in the atom from the tasks n and l is designated by the current rank: 1s, 2s, 2p, 3s, etc. Here the number indicates the value of the head quantum number, and the letter indicates the orbital quantum number: the symbols s, p, d, f indicate the values l = 0, 1, 2. 3, etc.
The light shines both on the Khvilov’s and on the corpuscular power. Khvil's power manifests itself when the light broadens (interference, diffraction). Corpuscular powers are revealed during the interaction of light with speech (photo-effect, vibration and polishing of light by atoms).
The power of a photon as a particle (energy E and momentum p) is associated with its power (frequency and power λ) with relationships
; , (19)
de h = 6.63 10 -34 J - Planck's constant.
Trying to solve the difficult Bohr model of the atom, the French physicist Louis de Broglie in 1924. presenting the hypothesis that the rise of the corpuscular and corpuscular powers of power is either light or any material body. Then the particles of speech (for example, electronics) linger under the influence of the Hvili authorities. Having determined the stew, it is from de Broglie to the skin body with a mass of m, which crumbles due to the fluidity of the υ, indicating a hwil process with a long hwil
The greatest power of the kingdom manifests itself in microobjects (elementary particles). As a result, the small mass of the dovzhin de Broglie extract appears leveled with a pressurized stand in the crystals. In these minds, when a beam of particles interacts with crystalline crystals, diffraction phenomena appear. Electrons with energy 150 eV Dovzhyna hvilya confirms λ»10 -10 m. The same order applies to interatomic formations in crystals. If a beam of such electrons is directed onto a crystal, the smell will be dissipated by the laws of diffraction. A diffraction pattern (electronogram) was recorded on a photographic camera and contains information about the existence of trivial crystalline orbits.
Malyunok 6 Illustration of the Khvil authorities of speech
To illustrate the power of particles, a clear experiment is often used - passing a beam of electrons (and other particles) through a gap of width Δx. According to the theory, after diffraction at the slit, the beam will widen with a wide spread θ»λ/Δх. From a corpuscular view, the widening of the beam after passing through the gap is explained by the appearance of a certain transverse impulse in the particles. Dispersion of the value of the transverse impulse (“insignificance”) є
(21)
Relationship (22)
There is a connection between insignificances. This interaction with the corpuscular world makes the manifestation of the power of the particles evident.
An experiment in which a beam of electrons passes through two closely spaced slits may provide a more striking illustration of the power of particles. This experiment is an analogue of Young's optical interference investigation.
4. 10 Quantum model of the atom Experimental facts (electron diffraction, the Compton effect, photographic effects and many others) and theoretical models, on the basis of the Bohr model of the atom, clearly indicate that the laws of classical physics become inappropriate for a description of the behavior of atoms and molecules and their interactions with light. Over a period of ten years between 1920 and 1930 pp. low data of physicists of the 20th century. (de Broglie, Heisenberg, Born, Schrödinger, Bohr, Pauli et al.) taking up a everyday theory to adequately describe the phenomena of the microworld. As a result, quantum mechanics was born, which became the basis of all current theories of everyday speech, one might say, the basis (at the same time as the theory of validity) of physics of the twentieth century.
The laws of quantum mechanics are stagnant in the microworld, while at the same time we live with macroscopic objects and live in the macroworld, which is governed by completely different, classical laws. It is not surprising that many of the principles of quantum mechanics cannot be overridden by us and are perceived as marvelous, impossible, insignificant. Timing is no less, quantum mechanics is, melodiously, the most confirmed theory to date, the fragments of the inheritance of the developments that follow the laws of this theory are victorious in almost everything that we know and have become part of human civilization (you can learn about those conductor elements, the work of which You can now read the text on the monitor screen, covering it with speech, which is also supported by quantum mechanics).
Unfortunately, the mathematical apparatus of quantum mechanics is becoming more complex and the ideas of quantum mechanics can only be expressed verbally and therefore insufficiently. With respect to this, we will try to make any statements about this idea.
The basic concepts of quantum mechanics are the concept of the quantum state of any microobject or microsystem (this may include a particle, an atom, a molecule, a collection of atoms, etc.).
Quantum model of the atom It appears from the planetary planet that its electron does not have exactly the same coordinates and fluidity, so it is worthless to talk about the trajectories of its movement. You can designate (and paint) only the interregions of your most important direction (orbitals).
The state of any microobject or microsystem (this can be a part, an atom, a molecule, a collection of atoms, etc.) can be characterized by the data of quantum numbers: the value of energy, momentum, moment of impulse, projection of this moment of impulse anyway, the charge is too bad.
SCHRÖDINGER'S RAVEN For the electron decay at the Coulomb field of the atomic nucleus, water is used to analyze the quantum model of the atom. As a result of this relationship, a complex function emerges, which is based not only on the coordinates of the hour t, but also on 4 parameters that can discretely set values and are called quantum numbers. The stinks are called: smut, azimuthal, magnetic and magnetic spin.
Golovne quantum number n You can type integer values 1, 2, ... . Von indicates the energy value of an electron in an atom
DE E i – ionization energy of the water atom (13.6 eV).
AZIMUTAL (ORBITAL) quantum number l
indicates the modulus of the angular momentum of the electron in its orbital region 
(24)
where s is a spin quantum number, which has only one value in a skin particle. For example, for an electron s = (similarly for a proton and neutron). For a photon s=1.
Virogenimi are called electron states with new energy.
CARDNESS VIROGENNIA There are a lot of stations with the same energy.
SHORT recording the electron in an atom: NUMBER, which is prior to the head quantum number, and the letter, which stands for the azimuthal quantum number:
Table 1 Short description of the electron in an atom
NNA COATING OF AN ATOM OF A CHEMICAL ELEMENT
§ 1. WEEKEND PRESENTATIONS OF QUANTUM MECHANICS
The theory of the atom lies in the laws that describe the range of microparticles (electrons, atoms, molecules) and systems (for example, crystals). The masses and sizes of microparticles are extremely small compared to the masses and sizes of macroscopic bodies. Therefore, the powers and laws governing the flow of the surrounding microparticles clearly differ from the powers and laws governing the flow of the macroscopic body, which follows classical physics. The dynamics and interactions of microparticles are described by quantum (or Hvili) mechanics. Vaughn relies on the discovery of quantization of energy, the whilian nature of the collapse of microparticles and the most modern (statistical) method for describing microobjects.
The quantum nature of the generation and degradation of energy. Approximately on the cob of the XX century. Investigations into a number of phenomena (vipromotion of baked bodies, photographic effects, atomic spectra) led to the discovery that energy is expanded and transmitted, absorbed and reverberated not continuously, but discretely, in separate portions - quanta. The energy of a system of microparticles can also be increased by multiples of quanta.
The concept of quantum energy was first discovered by M. Planck (1900) and later elaborated by A. Einstein (1905). Quantum energy? lie under the vibration frequency v:
de h - Planck's position)