The quasi-classical asymptotic solutions of some problems in mathematical physics
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 1 (1961) no. 1, pp. 113-128
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A suitable transformation of the dependent and independent variables in Schrödinger's time-dependent equation for the quantized state of a system of particles in a potential field leades to a linear equation. It is shown by using perturbation theory that this equation has a series solution in powers of $h$ (Planck's constant). In this way it is found to be possible to pass in the limit, as $h\to 0$, from quantum mechanics to classical mechanics. The existence of the total integral of the Hamilton-Jacobi equation is also discussed.
@article{ZVMMF_1961_1_1_a6,
author = {V. P. Maslov},
title = {The quasi-classical asymptotic solutions of some problems in mathematical physics},
journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
pages = {113--128},
publisher = {mathdoc},
volume = {1},
number = {1},
year = {1961},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZVMMF_1961_1_1_a6/}
}
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%0 Journal Article %A V. P. Maslov %T The quasi-classical asymptotic solutions of some problems in mathematical physics %J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki %D 1961 %P 113-128 %V 1 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/ZVMMF_1961_1_1_a6/ %G ru %F ZVMMF_1961_1_1_a6
V. P. Maslov. The quasi-classical asymptotic solutions of some problems in mathematical physics. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 1 (1961) no. 1, pp. 113-128. http://geodesic.mathdoc.fr/item/ZVMMF_1961_1_1_a6/