2D Schr\"odinger Equation with Singular Even-Power and Inverse-Power Potentials in Non Commutative Complex space

TL;DR

This paper derives exact solutions for the 2D Schrödinger equation with specific potentials in non-commutative complex space, revealing effects analogous to Zeeman splitting due to space non-commutativity.

Contribution

It provides exact solutions for a Schrödinger equation with singular potentials in non-commutative space, linking non-commutativity to magnetic effects on spin-1/2 particles.

Findings

Non-commutative space induces magnetic-like effects.

Solutions show energy spectrum shifts similar to Zeeman splitting.

Non-commutativity affects particle spin and energy levels.

Abstract

We obtain exact solutions of the 2D Schr\"odinger equation with the Singular Even-Power and Inverse-Power Potentials in non-commutative complex space, using the Power-series expansion method. Hence we can say that the Schr\"odinger equation in non-commutative complex space describes to the particles with spin (1/2)in an external uniform magnitic field. Where the noncommutativity play the role of magnetic field with created the total magnetic moment of particle with spin 1/2, who in turn shifted the spectrum of energy. Such effects are similar to the Zeeman splitting in a commutative space.