Abstract
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.
Original language | English (US) |
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Pages (from-to) | 543-554 |
Number of pages | 12 |
Journal | Journal of Difference Equations and Applications |
Volume | 19 |
Issue number | 4 |
DOIs | |
State | Published - Apr 2013 |
Keywords
- Heisenberg uncertainty principle
- Schrödinger group
- coherent and squeezed states
- dynamic invariants
- generalized harmonic oscillators
- time-dependent Schrödinger equation
ASJC Scopus subject areas
- Analysis
- Algebra and Number Theory
- Applied Mathematics