In 1924, the young French theoretical physicist Louis de Broglie introduced the concept of waves of matter into scientific circulation. This bold theoretical assumption extended the property of wave-particle duality (duality) to all manifestations of matter - not only radiation, but also 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 - de Broglie wave.
History of the birth of a concept
The semi-classical model of the atom proposed in 1913 by N. Bohr was based on two postulates:
- The moment of 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 the Planck constant, whose presence in the formula clearly indicates that the angular momentum of the particle is quantized. Consequently, in the atom there is a set of allowed orbits along which the electron can only move, and, being on them, it does not radiate, that is, does not lose energy.
- Radiation 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 energy corresponding to these orbits. Since there are no intermediate states between the allowed orbits, the radiation is also strictly quantized. Its frequency is (E 1 - E 2 ) / h, this directly follows from Planck's formula for energy E = hν.
So, the Bohr model of the atom “forbade” the electron to radiate in orbit and be between the orbits, however, its motion was considered classically, like the revolution of the planet around the Sun. De Broglie sought the answer to the question of why the electron behaves this way. Is it possible to naturally explain the presence of permissible orbits? He suggested that the electron must necessarily be accompanied by some wave. It is her presence that makes the particle "choose" only such orbits in which this wave is stacked an integer number of times. This was the meaning of the integer coefficient in the formula postulated by Bohr.
It follows 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 an atom.
Calculation of the wavelength associated with the particle
The young scientist received an extremely interesting relationship, which allows us to determine what these wave properties are. What is quantitatively de Broglie wave? The formula for its calculation has a simple form: λ = h / p. Here λ is the wavelength, and p is the particle momentum. For nonrelativistic particles, this ratio can be written as λ = h / mv, where m is the mass and v is the particle velocity.
Why this formula is of particular interest is evident from the quantities in it. De Broglie was able to combine in one ratio the particle and wave characteristics of matter — momentum and wavelength. And the Planck constant connecting them (its value is approximately equal to 6.626 × 10 -27 erg ∙ s or 6.626 × 10 -34 J ∙ s) sets the scale at which the wave properties of the substance appear.
"Waves of matter" in the micro- and macrocosm
So, the greater the momentum (mass, speed) of a physical object, the shorter the wavelength associated with it. This is the reason that macroscopic bodies do not show the wave component of their nature. As an illustration, it will be sufficient to determine the de Broglie wavelength for objects of various scales.
- Land. The mass of our planet is about 6 × 10 24 kg, the speed of movement in orbit relative to the Sun is 3 × 10 4 m / s. Substituting these values into the formula, we obtain (approximately): 6.6 × 10 -34 / (6 × 10 24 × 3 × 10 4 ) = 3.6 × 10 -63 m. It can be seen that the length of the “earth wave” is vanishingly small size. To any possibility of its registration, there are not even distant theoretical premises.
- Bacteria weighing about 10 -11 kg, moving at a speed of about 10 -4 m / s. Having made a similar calculation, you can find out that the de Broglie wave of one of the smallest living creatures 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 the electron be dispersed by a potential difference of 1 V to a speed of 10 6 m / s. Then the electron wavelength will be approximately 7 × 10 -10 m, or 0.7 nanometers, which is comparable with the lengths of x-ray waves and is quite amenable to registration.
The mass of the electron, like other particles, is so small, imperceptible that the other side of their nature becomes noticeable - the undulation.
Propagation speed
Distinguish concepts such as phase and group velocity of waves. The phase (the velocity of the surface of the same 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 does not belong to the number of objects through which information can be transmitted, so the causality principle in this case is not violated in any way.
The group velocity is less than the speed of light, it is associated with the displacement of the superposition (superposition) of many waves formed due to dispersion, and it reflects the speed of an electron or any other particle with which the wave is associated.
Experimental discovery
The magnitude of the de Broglie wavelength allowed physicists to carry out experiments confirming the assumption of the wave properties of matter. An answer to the question of whether electronic waves are real could be an experiment to detect the diffraction of the flux of these particles. For X-rays close to the electrons in wavelength, the usual diffraction grating is not suitable - its period (i.e. the distance between the dashes) is too long. Suitable period sizes are atomic sites of crystal lattices.
Already in 1927, K. Davisson and L. Jermer set up an experiment to detect electron diffraction. Nickel single crystal was used as a reflective lattice; the electron beam scattering intensity at different angles was recorded with a galvanometer. The nature of the scattering revealed a clear diffraction pattern confirming de Broglie's assumption. Regardless of Davisson and Germer, the same year, electron diffraction was experimentally discovered by J.P. Thomson. A somewhat later appearance of the diffraction pattern was found for proton, neutron, and atomic beams.
In 1949, a group of Soviet physicists led by V. Fabrikant conducted a successful experiment using not electrons, but individual electrons, which made it possible to prove irrefutably: diffraction is not an effect of the collective behavior of particles, and the wave properties belong to the electron as such.
The development of ideas about the "waves of matter"
L. de Broglie himself represented the wave as a real physical object, inextricably linked to the particle and controlling its motion, 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 the completely wave nature of matter, in fact, ignoring its corpuscular side. Any particle in Schrödinger's understanding 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” in space.
During the heated discussions of the mid 20-ies of the XX century, quantum physics has developed an approach that brings together the particle and wave patterns in the description of matter. Theoretically, it was justified by M. Born, and its essence in a few words can be expressed as follows: de Broglie wave reflects the probability distribution of a particle at a certain point at a certain point in time. Therefore, it is also called the wave of probability. Mathematically, it is described by the Schrödinger wave function , the solution of which allows one to obtain the amplitude of this wave. The square of the amplitude modulus determines the probability.
The meaning of the de Broglie wave hypothesis
The probabilistic approach, improved by N. Bohr and V. Heisenberg in 1927, formed the basis of the so-called Copenhagen interpretation, which became extremely productive, although its adoption was given to science at the cost of abandoning visual-mechanical, figurative models. Despite the presence of a number of controversial issues, such as the famous “measurement problem,” the further development of quantum theory with its many 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 of almost a hundred years ago about the “waves of matter”. Its essence, despite the changes in the original interpretation, remains undeniable: all matter has a dual nature, the various sides of which, always manifesting separately from each other, are nevertheless closely interconnected.