In 1924, the young French theoretical physicist Louis de Broglie introduced the concept of matter waves into scientific circulation. This bold theoretical assumption extended the property of wave-particle duality (duality) to all manifestations of matter - not only to radiation, but also to any particles of matter. And although modern quantum theory understands the “wave of matter” differently than the author of the hypothesis, this physical phenomenon associated with material particles bears his name - the de Broglie wave.
History of the birth of the concept
The semiclassical model of the atom proposed by N. Bohr in 1913 was based on two postulates:
- The angular momentum (momentum) of an electron in an atom cannot be anything. It is always proportional to nh/2π, where n is any integer starting from 1, and h is Planck's constant, the presence of which in the formula clearly indicates that the angular momentum of the particlequantized Consequently, there is a set of allowed orbits in the atom, along which only the electron can move, and, staying on them, it does not radiate, that is, does not lose energy.
- Emission or absorption of energy by an atomic electron occurs during the transition from one orbit to another, and its amount is equal to the difference in energies corresponding to these orbits. Since there are no intermediate states between allowed orbits, the radiation is also strictly quantized. Its frequency is (E1 – E2)/h, this directly follows from the Planck formula for the energy E=hν.
So, the Bohr model of the atom "prohibited" the electron from radiating in orbit and being between orbits, but its movement was considered classically, like the revolution of a planet around the Sun. De Broglie was looking for an answer to the question why the electron behaves the way it does. Is it possible to explain the presence of admissible orbits in a natural way? He suggested that the electron must be accompanied by some wave. It is its presence that makes the particle "choose" only those orbits on which this wave fits an integer number of times. This was the meaning of the integer coefficient in the formula postulated by Bohr.
It followed from the hypothesis that the de Broglie electron wave is not electromagnetic, and the wave parameters should be characteristic of any particles of matter, and not just electrons in the atom.
Calculating the wavelength associated with a particle
The young scientist got an extremely interesting ratio, which allowsdetermine what these wave properties are. What is the quantitative de Broglie wave? The formula for its calculation has a simple form: λ=h/p. Here λ is the wavelength and p is the momentum of the particle. For nonrelativistic particles, this ratio can be written as λ=h/mv, where m is the mass and v is the particle's velocity.
Why this formula is of particular interest can be seen from the values in it. De Broglie managed to combine in one ratio the corpuscular and wave characteristics of matter - momentum and wavelength. And the Planck constant connecting them (its value is approximately 6.626 × 10-27 erg∙s or 6.626 × 10-34 J∙ c) sets the scale at which the wave properties of matter appear.
"Waves of matter" in the micro- and macroworld
So, the greater the momentum (mass, speed) of a physical object, the shorter the wavelength associated with it. This is the reason why macroscopic bodies do not show the wave component of their nature. As an illustration, it will suffice to determine the de Broglie wavelength for objects of various scales.
- Earth. The mass of our planet is about 6 × 1024 kg, the orbital speed relative to the Sun is 3 × 104 m/s. Substituting these values into the formula, we get (approximately): 6, 6 × 10-34/(6 × 1024 × 3 × 10 4)=3.6 × 10-63 m. It can be seen that the length of the "earth wave" is a vanishingly small value. To any possibility of its registration there is not evenremote theoretical premises.
- A bacterium weighing about 10-11 kg, moving at a speed of about 10-4 m/s. Having made a similar calculation, one can find out that the de Broglie wave of one of the smallest living beings has a length of the order of 10-19 m - also too small to be detected.
- An electron having a mass of 9.1 × 10-31 kg. Let an electron be accelerated by a potential difference of 1 V to a speed of 106 m/s. Then the wavelength of the electron wave will be approximately 7 × 10-10 m, or 0.7 nanometers, which is comparable to the lengths of X-ray waves and quite amenable to registration.
The mass of an electron, like other particles, is so small, imperceptible, that the other side of their nature becomes noticeable - wavelike.
Spread rate
Distinguish between such concepts as phase and group velocity of waves. Phase (the speed of movement of the surface of identical phases) for de Broglie waves exceeds the speed of light. This fact, however, does not mean a contradiction with the theory of relativity, since the phase is not one of the objects through which information can be transmitted, so the principle of causality in this case is not violated in any way.
The group speed is less than the speed of light, it is associated with the movement of a superposition (superposition) of many waves formed due to dispersion, and it is she who reflects the speed of an electron or any other particle with which the wave is associated.
Experimental detection
The magnitude of the de Broglie wavelength allowed physicists to carry out experiments confirming the assumption about the wave properties of matter. The answer to the question of whether electron waves are real could be an experiment to detect the diffraction of a stream of these particles. For X-rays close in wavelength to electrons, the usual diffraction grating is not suitable - its period (that is, the distance between the strokes) is too large. Atomic nodes of crystal lattices have a suitable period size.
Already in 1927, K. Davisson and L. Germer set up an experiment to detect electron diffraction. A nickel single crystal was used as a reflective grating, and the intensity of electron beam scattering at different angles was recorded using a galvanometer. The nature of the scattering revealed a clear diffraction pattern, which confirmed de Broglie's assumption. Independently of Davisson and Germer, J. P. Thomson experimentally discovered electron diffraction in the same year. Somewhat later, the appearance of a diffraction pattern was established for proton, neutron, and atomic beams.
In 1949, a group of Soviet physicists led by V. Fabrikant conducted a successful experiment using not a beam, but individual electrons, which made it possible to irrefutably prove that diffraction is not any effect of the collective behavior of particles, and the wave properties belong to the electron as such.
Development of ideas about "waves of matter"
L. de Broglie himself imagined the wave asa real physical object, inextricably linked with a particle and controlling its movement, and called it a "pilot wave". However, while continuing to consider particles as objects with classical trajectories, he was unable to say anything about the nature of such waves.
Developing the ideas of de Broglie, E. Schrodinger came to the idea of a completely wave nature of matter, in fact, ignoring its corpuscular side. Any particle in the understanding of Schrödinger is a kind of compact wave packet and nothing more. The problem of this approach was, in particular, the well-known phenomenon of the rapid spreading of such wave packets. At the same time, particles, such as an electron, are quite stable and do not “smear” over space.
During the heated discussions of the mid-20s of the XX century, quantum physics developed an approach that reconciles the corpuscular and wave patterns in the description of matter. Theoretically, it was substantiated by M. Born, and its essence can be expressed in a few words as follows: the de Broglie wave reflects the distribution of the probability of finding a particle at a certain point at some point in time. Therefore, it is also called the probability wave. Mathematically, it is described by the Schrödinger wave function, the solution of which makes it possible to obtain the magnitude of the amplitude of this wave. The square of the modulus of the amplitude determines the probability.
The value of de Broglie's wave hypothesis
The probabilistic approach, improved by N. Bohr and W. Heisenberg in 1927, formed intothe basis of the so-called Copenhagen interpretation, which became extremely productive, although its adoption was given to science at the cost of abandoning visual-mechanistic, figurative models. Despite the presence of a number of controversial issues, such as the famous "problem of measurement", the further development of quantum theory with its numerous applications is associated with the Copenhagen interpretation.
Meanwhile, it should be remembered that one of the foundations of the indisputable success of modern quantum physics was de Broglie's brilliant hypothesis, a theoretical insight about "matter waves" almost a century ago. Its essence, despite changes in the original interpretation, remains undeniable: all matter has a dual nature, the various aspects of which, always appearing separately from one another, are nevertheless closely interconnected.
