The path integral on the Poincaré upper half-plane with a magnetic field and for the Morse potential
type: Item
instance of: scholarly article
title: The path integral on the Poincaré upper half-plane with a magnetic field and for the Morse potential
zbMATH Open document ID: 0652.58042
DOI: 10.1016/0003-4916(88)90283-7
author: Christian Grosche
published in: Annals of Physics
publication date: 1988-01-01T00:00:00Z
review text: Rigorous path integral treatments on the Poincaré upper half-plane with a magnetic field and for the Morse potential are presented. The calculation starts with the path integral on the Poincaré upper half- plane with a magnetic field. By a Fourier expansion and a non-linear transformation this problem is reformulated in terms of the path integral for the Morse potential. This latter problem can be reduced by an appropriate space-time transformation to the path integral for the harmonic oscillator with generalised angular momentum, a technique which has been developed in recent years. The well-known solution for the last problem enables one to give explicit expressions for the Feynman kernels for the Morse potential and for the Poincaré upper half-plane with magnetic field, respectively. The wavefunctions and the energy spectrum for the bound and scattering states are given, respectively.
Mathematics Subject Classification ID: 58Z05
Mathematics Subject Classification ID: 81S40
Mathematics Subject Classification ID: 58D30
zbMATH DE Number: 4064121
zbMATH Keywords: path integral
zbMATH Keywords: magnetic field
zbMATH Keywords: Morse potential
zbMATH Keywords: Feynman kernels
MaRDI profile type: Publication
full work available at URL: 0003-4916(88)90283-7
OpenAlex ID: W2116298188
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description: scientific article; zbMATH DE number 4064121