Geodesic
Comparison of Thermodynamic Characteristics of a Potential Well under Quantum and Classical Approaches
Funkcionalʹnyj analiz i ego priloženiâ, Tome 36 (2002) no. 3, pp. 48-55.

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The conjecture according to which the mean energy of an equilibrium system in quantum theory exceeds the mean energy of the corresponding classical system is considered. It is rigorously proved that the conjecture holds for the potential well. The estimates for the mean energy of the potential well at high and low temperatures are of special interest.
Keywords: equilibrium systems, mean energy, potential well. 
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L. A. Sakhnovich. Comparison of Thermodynamic Characteristics of a Potential Well under Quantum and Classical Approaches. Funkcionalʹnyj analiz i ego priloženiâ, Tome 36 (2002) no. 3, pp. 48-55. http://geodesic.mathdoc.fr/item/FAA_2002_36_3_a4/

[1] Landau L. D., Lifshits E. M., Statisticheskaya fizika, Nauka, M., 1964 | Zbl

[2] Sakhnovich L. A., “Sravnenie kvantovogo i klassicheskogo podkhodov v statisticheskoi fizike”, TMF, 123:3 (2000), 516–520 | DOI | MR | Zbl

[3] Evgrafov M. A., Asimptoticheskie otsenki i tselye funktsii, Gostekhizdat, M., 1957 | MR

[4] Kac M., “Can one hear the shape of a drum?”, Amer. Math. Monthly, 73:4 (1966), 1–23 | DOI | MR | Zbl

[5] Birman M. Sh., Solomyak M. Z., “Asimptotika spektra differentsialnykh uravnenii”, Itogi nauki i tekhniki. Matem. analiz, 14, VINITI, M., 1977, 5–58 | MR

[6] Fedosov B. V., “Asimptoticheskie formuly dlya sobstvennykh znachenii operatora Laplasa v sluchae poliedra”, DAN SSSR, 57 (1964), 536–538 | MR

[7] Van der Varden B. L., Algebra, Nauka, M., 1979 | MR