Coherent States in a Problem with Infinitely Multiple Spectrum

Abstract

The solutions of the Schrodinger (Schrodinger – Pauli) equations and the Dirac equation in the 2+1 space for the two-dimensional motion of a charged particle in a uniform and constant magnetic field, as well as the construction of coherent states based on the solutions obtained are considered. A specific feature of this problem is the presence of a discrete spectrum with infinite multiplicity of degeneracy. Two pairs of creation and annihilation operators allow one to construct coherent states which are a special superposition of the states of two oscillators. The influence of the multiplicity of the spectrum on the average values of coordinates and momenta due to the appearance of two pairs of creation and annihilation operators is shown. The constructed coherent states depending on two complex numbers lead to two independent Poisson distributions for two types of vibration quanta. The introduced operators allow one to represent the solutions of the Dirac equation in the 2+1 space for the discrete spectrum problem under consideration in a simple form.