Spin Non-commutativity and the Three-Dimensional Harmonic Oscillator

Abstract

A three-dimensional harmonic oscillator with spin non-commutativity in the phase space is considered. The system has a regular symplectic structure and by using supersymmetric quantum mechanics techniques, the ground state is calculated exactly. We find that this state is infinitely degenerate and it has explicit spontaneous broken symmetry. Analyzing the Heisenberg equations, we show that the total angular momentum is conserved.

6 pages, no figures,references added

References in corpus (5)

• Position-dependent noncommutativity in quantum mechanics
• Magnetic-Dipole Spin Effects in Noncommutative Quantum Mechanics
• Noncommutativity due to spin
• Towards a Noncommutative Astrophysics
• Aharonov-Bohm effect in a Class of Noncommutative Theories

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