-
- O. G. Smolyanov
- Faculty of Mechanics and Mathematics, Moscow State University, 119899 Moscow, Russia
-
- A. G. Tokarev
- Department of Mathematics, University of Wales Swansea, Singleton Park, Swansea SA2 8PP, United Kingdom
-
- A. Truman
- Department of Mathematics, University of Wales Swansea, Singleton Park, Swansea SA2 8PP, United Kingdom
説明
<jats:p>The main aim of the present paper is using a Chernoff theorem (i.e., the Chernoff formula) to formulate and to prove some rigorous results on representations for solutions of Schrödinger equations by the Hamiltonian Feynman path integrals (=Feynman integrals over trajectories in the phase space). The corresponding theorem is related to the original (Feynman) approach to Feynman path integrals over trajectories in the phase space in much the same way as the famous theorem of Nelson is related to the Feynman approach to the Feynman path integral over trajectories in the configuration space. We also give a representation for solutions of some Schrödinger equations by a series which represents an integral with respect to the complex Poisson measure on trajectories in the phase space.</jats:p>
収録刊行物
-
- Journal of Mathematical Physics
-
Journal of Mathematical Physics 43 (10), 5161-5171, 2002-10-01
AIP Publishing
