Energy characteristics of a system of quantum anharmonic oscillators

Authors: Fedyakov D.I.
Published in issue: #8(61)/2021
DOI: 10.18698/2541-8009-2021-8-730

Category: Physics | Chapter: Thermophysics and theoretical heat engineering

Keywords: quantum anharmonic oscillator, Lennard-Jones potential, energy spectrum, perturbation theory, potential energy, stationary Schrödinger equation, potential barrier, partition function, Helmholtz free energy
Published: 06.09.2021

The possibility of using the loaded anharmonic oscillator model for describing the lattice sites is proved. The energy spectrum of the loaded anharmonic oscillator is obtained. The applicability of perturbation theory to the description of shifts nonlinear in F in the energy spectrum of an anharmonic oscillator loaded with a constant external force F is proved, up to the fourth order. The dependence of the Helmholtz free energy on temperature is established for a system of loaded anharmonic quantum oscillators. The results obtained can be applied to solving problems in condensed matter physics; in particular, the developed method makes it possible to determine the parameters of intermolecular interaction potentials by macroscopic energy characteristics (Helmholtz free energy, internal energy).


[1] Kvasnikov I.A. Termodinamika i statisticheskaya fizika. T. 2. Teoriya ravnovesnykh sistem. Statisticheskaya fizika [Thermodynamics and statistical physics. Vol. 2. Theory of balanced systems]. Moscow, Editorial URSS Publ., 2002 (in Russ.).

[2] Kvasnikov I.A. Termodinamika i statisticheskaya fizika. T. 3. Teoriya neravnovesnykh sistem. Statisticheskaya fizika [Thermodynamics and statistical physics. Vol. 3. Statistical physics]. Moscow, Editorial URSS Publ., 2003 (in Russ.).

[3] Brandt N.B., Kul’bachinskiy V.A. Kvazichastitsy v fizike kondensirovannogo sostoyaniya [Quasiparticles in physics of condensed state]. Moscow, Fizmatlit Publ., 2007 (in Russ.).

[4] Gilyarov V.L., Slutsker A.I. Energy features of a loaded quantum anharmonic oscillator. FTT, 2010, vol. 52, no. 3, pp. 540–544 (in Russ.). (Eng. version: Phys. Solid State, 2010, vol. 52, no. 3, pp. 585–590. DOI: https://doi.org/10.1134/S1063783410030200)

[5] Animalu A.O. Intermediate quantum theory of crystalline solids. Prentice-Hall, 1978. (Russ. ed.: Kvantovaya teoriya kristallicheskikh tverdykh tel. Moscow, Mir Publ., 1981.)

[6] Feynman R.P. Statistical mechanics. A set of lectures. W.A. Benjamin, 1972. (Russ. ed.: Statisticheskaya mekhanika. Moscow, Mir Publ., 1978.)

[7] Landau L.D., Lifshits E.M. Teoreticheskaya fizika. T. 3. Nerelyativistskaya teoriya [Theoretical physics. Vol. 3. Nonrelativistic theory]. Moscow, Nauka Publ., 1989 (in Russ.).

[8] Fok V.A. Nachala kvantovoy mekhaniki [Elements of quantum mechanics]. Moscow, Mir Publ., 1974 (in Russ.).

[9] Dreizler R.M., Gross E.K.U. Density functional theory. Springer, 1990.

[10] Parr R., Yang W. Density functional theory of atoms and molecules. Oxford, 1989.

[11] Vargaftik N.B. Spravochnik po teplofizicheskim svoystvam gazov i zhidkostey [Handbook on thermophysical properties of gases and liquids]. Moscow, Nauka Publ., 1972 (in Russ.).