Feynman path integrals for the inverse quartic oscillator. (English) Zbl 1152.81555
Author’s summary: The Feynman path integral representation for the weak solution of the Schrödinger equation with an inverse quartic oscillator potential is given in terms of a well defined infinite dimensional oscillatory integral. An analytically continued Wiener integral representation for the solution is provided and an explicit description of the quantum dynamics associated with a nonessentially self-adjoint Hamiltonian is given.
MSC:
| 81S40 | Path integrals in quantum mechanics |
| 47N50 | Applications of operator theory in the physical sciences |
| 58D30 | Applications of manifolds of mappings to the sciences |
| 60B11 | Probability theory on linear topological spaces |
Keywords:
Feynman path integrals; Schrödinger equation; analytic continuation of Wiener integrals; quartic oscillatorReferences:
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