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Probabilistic representation of solutions of Schrödinger equations

Zhi Chan Li, Ren Song

Jan 1, 19860 citations

The probabilistic solution of the third boundary value problem for the Schrödinger equation and its path integral representation

Vassilis G. Papanicolaou

University Microfilms International eBooksJan 1, 19880 citations

A Probabilistic Representation of the Cauchy Problem Solution for the Multidimensional Schrödinger Equation

Pavel Ievlev

Journal of Mathematical SciencesJan 8, 20203 citations

On the representation of contextual probabilistic dynamics in the complex Hilbert space: Linear and nonlinear evolutions, Schrödinger dynamics

Andrei Yu. Khrennikov

Il Nuovo Cimento BJan 1, 20051 citation

Томография центра масс и вероятностное представление квантовых состояний в приложении к задачам о туннелировании

A. S. Arkhipov, Юрий Ефремович Лозовик, Yu. E. Lozovik +2 more

Теоретическая и математическая физикаJan 1, 20051 citation

Symplectically covariant Schrödinger equation in phase space

Maurice A. de Gosson

A classical theorem of Stone and von Neumann says that the Schrödinger representation is, up to unitary equivalences, the only irreducible representation of the Heisenberg group on the Hilbert space of square-integrable functions on configuration space. Using the Wigner-Moyal transform we construct an irreducible representation of the Heisenberg group on a certain Hilbert space of square-integrable functions defined on phase space. This allows us to extend the usual Weyl calculus into a phase-space calculus and leads us to a quantum mechanics in phase space, equivalent to standard quantum mechanics. We also briefly discuss the extension of metaplectic operators to phase space and the probabilistic interpretation of the solutions of the phase space Schrödinger equationA classical theorem of Stone and von Neumann says that the Schrödinger representation is, up to unitary equivalences, the only irreducible representation of the Heisenberg group on the Hilbert space of square-integrable functions on configuration space. Using the Wigner-Moyal transform we construct an irreducible representation of the Heisenberg group on a certain Hilbert space of square-integrable functions defined on phase space. This allows us to extend the usual Weyl calculus into a phase-space calculus and leads us to a quantum mechanics in phase space, equivalent to standard quantum mechanics. We also briefly discuss the extension of metaplectic operators to phase space and the probabilistic interpretation of the solutions of the phase space Schrödinger equation

arXiv:math-ph/0505073Journal of Physics A Mathematical and GeneralOct 5, 200547 citations

Вероятностное представление квантовых эволюций

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Вероятностное представление квантовых эволюций

Abstract

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