The path integral on the Poincaré upper half-plane with a magnetic field and for the Morse potential
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.
scientific article; zbMATH DE number 4064121
scientific article