Abstract:
Quantum equation of motion for a particle in external field is written down in
the form of the integral equation of the Lippmann–Schwinger type, in which the
free solution term is replaced by the solution of the corresponding classical problem.
The iterations of the equation give quantum corrections to the classical solutions.
Citation:
Yu. M. Shirokov, “Perturbation theory with respect to Planck's constant”, TMF, 31:3 (1977), 327–332; Theoret. and Math. Phys., 31:3 (1977), 488–492
\Bibitem{Shi77}
\by Yu.~M.~Shirokov
\paper Perturbation theory with respect to Planck's constant
\jour TMF
\yr 1977
\vol 31
\issue 3
\pages 327--332
\mathnet{http://mi.mathnet.ru/tmf3031}
\transl
\jour Theoret. and Math. Phys.
\yr 1977
\vol 31
\issue 3
\pages 488--492
\crossref{https://doi.org/10.1007/BF01030565}
Linking options:
https://www.mathnet.ru/eng/tmf3031
https://www.mathnet.ru/eng/tmf/v31/i3/p327
This publication is cited in the following 8 articles:
Donald C Chang, “Physical interpretation of Planck's constant based on the Maxwell theory”, Chinese Phys. B, 26:4 (2017), 040301
O. I. Zavialov, “Relativistic Wigner Function and Nonlinear Representations of the Lorentz Group”, Proc. Steklov Inst. Math., 228 (2000), 126–134
N. M. Atakishiyev, Sh. M. Nagiyev, K. B. Wolf, “Wigner distribution functions for a relativistic linear oscillator”, Theoret. and Math. Phys., 114:3 (1998), 322–334
V. L. Kamskiǐ, Yu. V. Medvedev, V. S. Filinov, “A method of stochastic dynamics in the Wigner formulation of quantum mechanics”, Comput. Math. Math. Phys., 36:7 (1996), 923–934
G W Bund, “Classical distribution functions derived from Wigner distribution functions”, J. Phys. A: Math. Gen., 28:13 (1995), 3709
Herbert Steinrück, “Asymptotic analysis of the quantum Liouville equation”, Math Methods in App Sciences, 13:2 (1990), 143
G. K. Tolokonnikov, “Algebras of observables of nearly canonical physical theories. II”, Theoret. and Math. Phys., 61:2 (1984), 1072–1077
Yu. M. Shirokov, “Unified formalism for quantum and classical scattering theories”, Theoret. and Math. Phys., 38:3 (1979), 206–211
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