Infinite Dimensional Analysis Quantum Probability and Related Topics

FUNCTIONAL-INTEGRAL SOLUTION FOR THE SCHRÖDINGER EQUATION WITH POLYNOMIAL POTENTIAL: A WHITE NOISE APPROACH

Sonia Mazzucchi

Published Dec 1, 2011• 12 citations

Abstract

A functional integral representation for the weak solution of the Schrödinger equation with polynomially growing potentials is proposed in terms of a white noise functional.

DOI: 10.1142/s0219025711004572

Related papers

Feynman integrals for a class of exponentially growing potentials

Tobias Kuna, Ludwig Streit, Werner Westerkamp

We construct the Feynman integrands for a class of exponentially growing time-dependent potentials as white noise functionals. We show that they solve the Schrödinger equation. The Morse potential is considered as a special case.

arXiv:math-ph/0303022Journal of Mathematical PhysicsSep 1, 199828 citations

Feynman integrals for a class of exponentially growing potentials

Kuna, T, Ludwig Streit, Westerkamp, W

We construct the Feynman integrands for a class of exponentially growing time-dependent potentials as white noise functionals. We show that they solve the Schrodinger equation. The Morse potential is considered as a special case. (C) 1998 American Institute of Physics.

Jan 1, 199835 citations

ON A "HAMILTONIAN PATH-INTEGRAL" DERIVATION OF THE SCHRODINGER EQUATION (Spectral-scattering theory and related topics)

淳井上

数理解析研究所講究録May 1, 19980 citations

ON A "HAMILTONIAN PATH-INTEGRAL" DERIVATION OF THE SCHRODINGER EQUATION (Spectral-scattering theory and related topics)

Atsushi Inoue

数理解析研究所講究録May 1, 19980 citations

ANALYTICAL SOLUTION OF THE POSITION DEPENDENT MASS SCHR\"{O}DINGER EQUATION WITH A HYPERBOLIC TANGENT POTENTIAL

Abdelwahab Kharab, Hichem Eleuch

An analytical solution of the position dependent mass Schrödinger equation with a hyperbolic tangent potential is presented.The state energy and the corresponding wave function are obtained using the Nikiforov-Uvarov method.The energy eigenvalues and eigenfunctions are discussed and results are presented for some values of potential parameters.

International Journal of Apllied MathematicsMay 13, 20191 citation

Representation of solutions of the stochastic Schrödinger equation in the form of a Feynman integral

O. O. Obrezkov

Journal of Mathematical SciencesApr 16, 20085 citations