AN APPROACH TO SOLUTION OF THE SCHRÖDINGER EQUATION USING FOURIER-TYPE FUNCTIONALS

Title & Authors
AN APPROACH TO SOLUTION OF THE SCHRÖDINGER EQUATION USING FOURIER-TYPE FUNCTIONALS
Chang, Seung Jun; Choi, Jae Gil; Chung, Hyun Soo;

Abstract
In this paper, we consider the Fourier-type functionals on Wiener space. We then establish the analytic Feynman integrals involving the $\small{{\diamond}}$-convolutions. Further, we give an approach to solution of the Schr$\small{\ddot{o}}$dinger equation via Fourier-type functionals. Finally, we use this approach to obtain solutions of the Schr$\small{\ddot{o}}$dinger equations for harmonic oscillator and double-well potential. The Schr$\small{\ddot{o}}$dinger equations for harmonic oscillator and double-well potential are meaningful subjects in quantum mechanics.
Keywords
Schr$\small{\ddot{o}}$dinger equation;harmonic oscillator;double-well potential;Fourier-type functional;Feynman-Kac formula;Fourier transform;
Language
English
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3.
Relationships Involving Transforms and Convolutions Via the Translation Theorem, Stochastic Analysis and Applications, 2014, 32, 2, 348
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