Explanation

phonon is the quantum of normal mode of lattice vibration. The lattice has periodicity, so the vibration mode of the lattice takes the form of waves, known as lattice waves. A lattice wave represents a vibrational mode in which all atoms in a crystal participate. Atoms always vibrate around their equilibrium position. These atoms are interconnected through their mutual forces. In general, the interaction force between atoms can be well approximated as an elastic force, which makes the vibration propagate in crystal in the form of elastic wave. This vibration can theoretically be considered as a series of fundamental vibrations, namely the superposition of normal vibrations. When the amplitude of atomic vibration is small relative to the atomic spacing, it means that the modes of normal vibration can be approximated as independent. In other words, each normal vibration mode is actually a elastic wave with a specific frequency, wavelength and certain propagation direction, and the whole system is equivalent to a series of mutually independent harmonic oscillators. The energy of these harmonic oscillators will be continuous. According to quantum mechanics, their energy must be quantized, and only discrete values of integer times can be taken, that is, E_ N=(n+1/2) ?ω， Where n is a non negative integer, ? Is the reduced Planck constant, ω Is the vibration frequency of the lattice wave. These energy states E_ N can be considered to be composed of multiple energies ?ω And the smallest unit of this quantized elastic wave is called phonon. phonon is the collective of all atoms, not the quantum of the motion mode of an individual atom. phonon is a kind of quasi particle with space coordinate parameters and momentum. Since the chemical potential is zero, the phonon obeys Bose Einstein statistics and is a boson. Because it is a quasi particle, it does not have real mass, nor can phonon be taken from the crystal, so phonon cannot be simply equated with a simple harmonic oscillator in the lattice vibration. phonon itself does not have physical momentum, but it carries quasi momentum, lattice wave vector represents phonon wave vector, and has energy ?ω (Among them ? Is the reduced Planck constant, ω Is the vibration frequency of the lattice wave. This energy does not belong to a specific atom, but represents a collective excitation that has particle properties. The excited state of the harmonic oscillator can contain any number of phonon, so the number of phonon can generate and disappear from each other. The conservation law of phonon momentum is also different from that of ordinary particles, and phonon cannot exist without crystal. phonon is just a lattice wave excited quantum, which is called collective oscillation elementary excitation or quasiparticle.

Classification