Two new integrable cases of two-dimensional quantum mechanics with a magnetic field

Abstract

Two integrable cases of two-dimensional Schrödinger equation with a magnetic field are proposed. Using the polar coordinates and the symmetrical gauge, we will obtain solutions of these equation through Biconfluent and Confluent Heun functions. The quantization rules will be derived for both systems under consideration.

7 pages, few mistakes eliminated

References in corpus (2)

• Exact solution of the Schrödinger equation for the inverse square root potential $V_0/\sqrt{x}$
• Integrable and superintegrable quantum systems in a magnetic field

Cited by in corpus (2)

• Thermodynamic properties of a charged particle in non-uniform magnetic field
• Pair production of scalars around near-extremal Kerr-Sen black holes