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.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.

Journal of the Korean Mathematical SocietyMar 1, 201310 citations

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.