2D Schr\"odinger Equation with Mixed Potential in Noncommutaive Complex space

TL;DR

This paper derives exact solutions for the 2D Schrödinger equation with mixed potentials in noncommutative complex space, revealing magnetic-like effects and energy spectrum shifts similar to Zeeman splitting.

Contribution

It introduces exact solutions for the 2D Schrödinger equation in noncommutative complex space with mixed potentials, highlighting magnetic effects due to noncommutativity.

Findings

Noncommutativity acts like a magnetic field.

Energy spectrum experiences Zeeman-like splitting.

Exact solutions obtained using power-series expansion.

Abstract

We obtain exact solutions of the 2D Schr\"odinger equation for Hydrogen atom with the lenear and Harmonic Potentials in noncommutative complex space, using the Power-series expansion method. Hence we can say that the Schr\"odinger equation in noncommutative 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.