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International Journal of Modern Physics A

Electron propagator solution for an inhomogeneous magnetic field in the momentum space representation

H. Hamdi, H. Benzair

Published Sep 3, 2020• 1 citation
Publisher

Abstract

The relativistic quantum mechanics of the electron in an inhomogeneous magnetic field problem is solved exactly in terms of the momentum space path integral formalism. We adopt the space–time transformation methods, which are [Formula: see text]-point discretization dependent, to evaluate quantum corrections. The propagator is calculated, the energy eigenvalues and their associated curves are illustrated. The limit case is then deduced for a small parameter.

DOI
10.1142/s0217751x2050150x

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The relativistic quantum mechanics of the electron in an inhomogeneous magnetic field problem is solved exactly in terms of the momentum space path integral formalism. We adopt the space–time transformation methods, which are [Formula: see text]-point discretization dependent, to evaluate quantum corrections. The propagator is calculated, the energy eigenvalues and their associated curves are illustrated. The limit case is then deduced for a small parameter.
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In this work, we present a rigorous and complete non-relativistic treatment of the problem of a diatomic molecule which moves under the Hua potential in a D-dimensional Euclidean space. The radial Green’s function associated with this potential is constructed within the framework of the Feynman path integral. Different cases of this potential which are distinguished by the values of the deformation parameter q are considered separately. For [Formula: see text] q < 1 and r ∈ ] r0, +∞[, we adopt an appropriate Pekeris-type approximation for the centrifugal potential term to obtain the approximate spectrum of bound states lD ≠ 0. Some numerical results of the energy levels of certain diatomic molecules are calculated by using the correct minimum value of the deformation parameter q given by [Formula: see text]. For q < 0 or [Formula: see text], the problem is solvable only in a three-dimensional space. In both cases, the energy quantization condition is a transcendental equation that can be solved numerically. In the limit [Formula: see text], the energy spectrum and the corresponding wave functions of the radial Morse potential are regained.