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http://dx.doi.org/10.4134/JKMS.2013.50.2.259

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

Chang, Seung Jun (Department of Mathematics Dankook University)
Choi, Jae Gil (Department of Mathematics Dankook University)
Chung, Hyun Soo (Department of Mathematics Dankook University)
Publication Information
Journal of the Korean Mathematical Society / v.50, no.2, 2013 , pp. 259-274 More about this Journal
Abstract
In this paper, we consider the Fourier-type functionals on Wiener space. We then establish the analytic Feynman integrals involving the ${\diamond}$-convolutions. Further, we give an approach to solution of the Schr$\ddot{o}$dinger equation via Fourier-type functionals. Finally, we use this approach to obtain solutions of the Schr$\ddot{o}$dinger equations for harmonic oscillator and double-well potential. The Schr$\ddot{o}$dinger equations for harmonic oscillator and double-well potential are meaningful subjects in quantum mechanics.
Keywords
Schr$\ddot{o}$dinger equation; harmonic oscillator; double-well potential; Fourier-type functional; Feynman-Kac formula; Fourier transform;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
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