One-Dimensional Harmonic Oscillator in Quantum Phase Space
Within the framework of the quantum phase space representation established by Torres-Vega and Frederick, we solve the rigorous solutions of the stationary Schrödinger equations for the one-dimensional harmonic oscillator by means of the quantum wave-mechanics method. The result shows that the wave mechanics and the matrix mechanics are equivalent in phase space, just as in position or momentum space.
J. Lu et al., "One-Dimensional Harmonic Oscillator in Quantum Phase Space", Applied Mechanics and Materials, Vols. 110-116, pp. 3750-3754, 2012