The algebraic method for two-dimensional quantum atomic systems
The authors propose an easy and effective variant of the realization of the dynamical symmetry of hydrogen-like atoms in two-dimensional space, based on the relationship between the Schrodinger equation for the isotropic harmonic oscillator in one-dimensional complex space and the Schrodinger equation for the one-electron atom in two-dimensional space, that permits them to use the operator method to solve the Schrodinger equation for the two-dimensional atomic system. For illustration of the algebraic method, they consider the problem of the two-dimensional hydrogenic donor in a magnetic field. By the use of the path integral they also establish the relationship between the two-dimensional Coulomb Green function and the Green function for the isotropic harmonic oscillator in one-dimensional complex space.
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