On a Hidden Symmetry of Quantum Harmonic Oscillators

Details On a Hidden Symmetry of Quantum Harmonic Oscillators On a Hidden Symmetry of Quantum Harmonic Oscillators

2011-12-12

arxiv.org/abs/1112.2586v2

Physics

Quantum Physics

11 pages, 20 figures

Scientific paper

We consider a six-parameter family of the square integrable wave functions for the simple harmonic oscillator, which cannot be obtained by the standard separation of variables. They are given by the action of the corresponding maximal kinematical invariance group on the standard solutions. In addition, the phase space oscillations of the electron position and linear momentum probability distributions are computer animated and some possible applications are briefly discussed. A visualization of the Heisenberg Uncertainty Principle is presented.

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