On a Hidden Symmetry of Quantum Harmonic Oscillators
arXiv:1112.2586
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.
11 pages, 20 figures
References in corpus (7)
- Atomic physics and quantum optics using superconducting circuits
- The Cauchy Problem for a Forced Harmonic Oscillator
- The time-dependent Schroedinger equation, Riccati equation and Airy functions
- Soliton-like Solutions for Nonlinear Schroedinger Equation with Variable Quadratic Hamiltonians
- Representations of the Schrödinger group and matrix orthogonal polynomials
- On Integrability of Nonautonomous Nonlinear Schroedinger Equations
- The Berry Phase for Simple Harmonic Oscillators