Quantum Hamiltonian and Spectrum of Schrödinger Equation with Companied Harmonic Oscillator Potential and its Inverse in Both Three Dimensional Non-commutative Real Space and Phase

Abstract

In present search, we have studied the effect of the both non commutativity of three dimensional space and phase on the Schrödinger equation with companied Harmonic oscillator potential and it’s inverse, know by isotopic Harmonic oscillator plus inverse quadratic (h.p.i.) potential, we shown that the Hermitian NC Hamiltonian formed anisotropic operator and described many physics phenomena’s, we have also derived the exact degenerated spectrum for studied potential in the first order of two infinitesimal parameters Θ and associated for noncommutative space and phase, respectively.

Keywords

• The isotropic harmonic oscillator plus inverse quadratic potential and non-commutative space-phase
• Boopp’s shift method
• Schrödinger equatio