Annals of Functional Analysis

Applications of an analogue of conditional Wiener integrals

Seung Jun Chang, Hyun Soo Chung, and Il Yong Lee

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In this paper, we obtain formulas for the analogue of conditional Wiener integrals for the functional $F$ of the form $$ F(x) = \exp\Big\{ \int_{0}^{T} V(x(t)) dt \Big\}, \quad x\in C[0,T] $$ where $V: \Bbb{R} \rightarrow \Bbb{R}$ is a potential function. We then apply this formula to obtain several integration formulas for the functionals involving various potential functions which is used in quantum mechanics and other physical theories.

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Ann. Funct. Anal., Volume 6, Number 2 (2015), 116-132.

First available in Project Euclid: 19 December 2014

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Zentralblatt MATH identifier

Primary: 60J65: Brownian motion [See also 58J65]
Secondary: 28C20: Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) [See also 46G12, 58C35, 58D20, 60B11] 43A32: Other transforms and operators of Fourier type

Pöschl--Teller potential analogue of conditional Wiener integral simple formula harmonic oscillator double-well potential


Lee, Il Yong; Chung, Hyun Soo; Chang, Seung Jun. Applications of an analogue of conditional Wiener integrals. Ann. Funct. Anal. 6 (2015), no. 2, 116--132. doi:10.15352/afa/06-2-11.

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