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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Abstract

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.

Article information

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

Dates
First available in Project Euclid: 19 December 2014

Permanent link to this document
https://projecteuclid.org/euclid.afa/1418997771

Digital Object Identifier
doi:10.15352/afa/06-2-11

Mathematical Reviews number (MathSciNet)
MR3292520

Zentralblatt MATH identifier
1347.60098

Subjects
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

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

Citation

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. https://projecteuclid.org/euclid.afa/1418997771


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