Harmonic-oscillator phase operators

Berry phase in the simple harmonic oscillator

Berry phase of simple harmonic oscillator is considered in a general representation. It is shown that, Berry phase which depends on the choice of representation can be defined under evolution of the half of period of the classical motions, as well as under evolution of the period. The Berry phases do not depend on the mass or angular frequency of the oscillator. The driven harmonic oscillator i...

Relativistic Ladder Operators for the Three-Dimensional Harmonic Oscillator

The quantum constraint equations for a relativistic three-dimensional harmonic oscillator are shown to find concise expression in terms of Lorentz covariant ladder operators. These ladder operators consist of two conjugate 4-vectors that are each constrained to generate three linearly independent combinations of ladder operator components for raising and lowering the eigenstates of the oscillat...

Eigenvalue Problem for Schrödinger Operators and Time-Dependent Harmonic Oscillator

It is shown that the eigenvalue problem for the Hamiltonians of the standard form, H = p/(2m) + V (x), is equivalent to the classical dynamical equation for certain harmonic oscillators with time-dependent frequency. This is another indication of the central role played by time-dependent harmonic oscillators in quantum mechanics. The utility of the known results for eigenvalue problem in the so...

Harmonic Oscillator

PPV-HB: Harmonic Balance for Oscillator/PLL Phase Macromodel

A unique feature of oscillators is that small but sustained external perturbations lead to unboundedly large changes in phase, thereby making standard harmonic balance (HB) inapplicable to realistic oscillator phase macromodels. In this paper, we rectify this situation by presenting a novel extension of HB that is capable of handling oscillator phase macromodels. Key to the new method, termed P...