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J. Korean Math. Soc. 2013; 50(2): 259-274
Printed March 1, 2013
https://doi.org/10.4134/JKMS.2013.50.2.259
Copyright © The Korean Mathematical Society.
An approach to solution of the Schr\"{o}dinger equation using Fourier-type functionals
Seung Jun Chang, Jae Gil Choi, and Hyun Soo Chung
Dankook University, Dankook University, Dankook University
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\"{o}dinger equation via Fourier-type functionals. Finally, we use this approach to obtain solutions of the Schr\"{o}dinger equations for harmonic oscillator and double-well potential. The Schr\"{o}dinger equations for harmonic oscillator and double-well potential are meaningful subjects in quantum mechanics.
Keywords: Schr\"{o}dinger equation, harmonic oscillator, double-well potential, Fourier-type functional, Feynman-Kac formula, Fourier transform
MSC numbers: Primary 60J65, 81Q05, 28C20, 46C07
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