E G Thrapsaniotis 2008 J. Phys. A: Math. Theor. 41 205202 doi:10.1088/1751-8113/41/20/205202
Path integral methods via the use of the central limit theorem and application
E G Thrapsaniotis
Show affiliationsWe consider a path integral in the phase space possibly with an influence functional in it and we use a method based on the use of the central limit theorem on the phase of the path integral representation to extract an equivalent expression which can be used in numerical calculations. Moreover we give conditions under which we can extract closed analytical results. As a specific application we consider a general system of two coupled and forced harmonic oscillators with coupling of the form x1xα2 and we derive the relevant sign solved propagator.
- PACS
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03.65.Ge Solutions of wave equations: bound states
- MSC
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15A18 Eigenvalues, singular values, and eigenvectors
81S30 Phase space methods including Wigner distributions, etc.
60F05 Central limit and other weak theorems
- Subjects
- Dates
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Issue 20 (23 May 2008)
Received 8 October 2007, in final form 23 March 2008
Published 24 April 2008
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Path integral methods via the use of the central limit theorem and application
E G Thrapsaniotis 2008 J. Phys. A: Math. Theor. 41 205202
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