Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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AN APPROACH TO SOLUTION OF THE SCHRÖDINGER EQUATION USING FOURIER-TYPE FUNCTIONALS

  • Received : 2011.12.06
  • Published : 2013.03.01
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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 ${\diamond}$-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.

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References

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