• Title/Summary/Keyword: Feynman functional

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

  • Chang, Seung Jun;Choi, Jae Gil;Chung, Hyun Soo
    • Journal of the Korean Mathematical Society
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    • v.50 no.2
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    • pp.259-274
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    • 2013
  • 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.