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AN APPROACH TO SOLUTION OF THE SCHRÖDINGER EQUATION USING FOURIER-TYPE FUNCTIONALS
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 Title & Authors
AN APPROACH TO SOLUTION OF THE SCHRÖDINGER EQUATION USING FOURIER-TYPE FUNCTIONALS
Chang, Seung Jun; Choi, Jae Gil; Chung, Hyun Soo;
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 Abstract
In this paper, we consider the Fourier-type functionals on Wiener space. We then establish the analytic Feynman integrals involving the -convolutions. Further, we give an approach to solution of the Schrdinger equation via Fourier-type functionals. Finally, we use this approach to obtain solutions of the Schrdinger equations for harmonic oscillator and double-well potential. The Schrdinger equations for harmonic oscillator and double-well potential are meaningful subjects in quantum mechanics.
 Keywords
Schrdinger equation;harmonic oscillator;double-well potential;Fourier-type functional;Feynman-Kac formula;Fourier transform;
 Language
English
 Cited by
1.
Analytic Feynman integrals of functionals in a Banach algebra involving the first variation, Chinese Annals of Mathematics, Series B, 2016, 37, 2, 281  crossref(new windwow)
2.
A Modified Analytic Function Space Feynman Integral and Its Applications, Journal of Function Spaces, 2014, 2014, 1  crossref(new windwow)
3.
Relationships Involving Transforms and Convolutions Via the Translation Theorem, Stochastic Analysis and Applications, 2014, 32, 2, 348  crossref(new windwow)
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