Itogi Nauki i Tekhniki. Seriya "Teoriya Veroyatnostei. Matematicheskaya Statistika. Teoreticheskaya Kibernetika"
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Itogi Nauki i Tekhniki. Seriya "Teoriya Veroyatnostei. Matematicheskaya Statistika. Teoreticheskaya Kibernetika", 1978, Volume 15, Pages 5–78 (Mi intv35)  
This article is cited in 8 scientific papers (total in 8 papers)

Jump-type processes and their applications in quantum mechanics

V. P. Maslov, A. M. Chebotarev
Full-text PDF (3662 kB) Citations (8)
Abstract: A survey is presented of mathematical methods in the theory of the Feynman path integral. Principal attention is devoted to new results making it possible to represent the solution of the Cauchy problem for the Schrödinger equation and a quasilinear equation of Hartree type in the form of the mathematical expectation of functionals on jump-type Markov processes and to use Monte Carlo methods for solving these equations. A brief survey of results on complex Markov chains is presented.
English version:
Journal of Soviet Mathematics, 1980, Volume 13, Issue 3, Pages 315–358
DOI: https://doi.org/10.1007/BF01088985
Bibliographic databases:
UDC: 987.3:512.245
Language: Russian
Citation: V. P. Maslov, A. M. Chebotarev, “Jump-type processes and their applications in quantum mechanics”, Itogi Nauki i Tekhniki. Ser. Teor. Veroyatn. Mat. Stat. Teor. Kibern., 15, VINITI, Moscow, 1978, 5–78; J. Soviet Math., 13:3 (1980), 315–358
Citation in format AMSBIB
\Bibitem{MasChe78}
\by V.~P.~Maslov, A.~M.~Chebotarev
\paper Jump-type processes and their applications in quantum mechanics
\serial Itogi Nauki i Tekhniki. Ser. Teor. Veroyatn. Mat. Stat. Teor. Kibern.
\yr 1978
\vol 15
\pages 5--78
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/intv35}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=503258}
\zmath{https://zbmath.org/?q=an:0516.28016}
\transl
\jour J. Soviet Math.
\yr 1980
\vol 13
\issue 3
\pages 315--358
\crossref{https://doi.org/10.1007/BF01088985}
Linking options:
  • https://www.mathnet.ru/eng/intv35
  • https://www.mathnet.ru/eng/intv/v15/p5
    • This publication is cited in the following 8 articles:
    1. Mark Santer, Uwe Manthe, Gerhard Stock, “Quantum-classical Liouville description of multidimensional nonadiabatic molecular dynamics”, The Journal of Chemical Physics, 114:5 (2001), 2001  crossref
    2. WATARU ICHINOSE, “ON CONVERGENCE OF THE FEYNMAN PATH INTEGRAL FORMULATED THROUGH BROKEN LINE PATHS”, Rev. Math. Phys., 11:08 (1999), 1001  crossref
    3. T. C. Schmidt, K. Möhring, “Stochastic path-integral simulation of quantum scattering”, Phys. Rev. A, 48:5 (1993), R3418  crossref
    4. A. A. Konstantinov, V. P. Maslov, A. M. Chebotarev, “Probability representations of solutions of the Cauchy problem for quantum mechanical equations”, Russian Math. Surveys, 45:6 (1990), 1–26  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    5. S. M. Eleutério, R. Vilela Mendes, “Stochastic models for lattice gauge theories”, Z. Phys. C - Particles and Fields, 34:4 (1987), 451  crossref
    6. Ph. Blanchard, Ph. Combe, M. Sirugue, M. Sirugue-Collin, Lecture Notes in Physics, 262, Stochastic Processes in Classical and Quantum Systems, 1986, 87  crossref
    7. R.Vilela Mendes, “Stochastic mechanics, non-local potentials and jump processes”, Physics Letters A, 113:4 (1985), 187  crossref
    8. P. Blanchard, P. Combe, M. Sirugue, M. Sirugue-Collin, Lecture Notes in Mathematics, 1136, Quantum Probability and Applications II, 1985, 104  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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