Quantum oscillator in an infinite-particle harmonic system

E. Verboven

André F. Verbeure, E. Verboven

Michele Cini

Richard W. Robinett

The classical and quantum probability distributions for both position and momentum are compared for several model systems admitting bound states including the harmonic oscillator, the infinite well, and the linear confining potential (V(x)=F‖x‖). Examples corresponding to unbound systems, including the uniformly accelerating particle and the motion of a particle moving away from a point of unstable equilibrium, i.e., the ‘‘unstable oscillator’’ defined by V(x)=−kx2/2, are also considered. The quantum and classical distribution of kinetic and potential energy for the harmonic oscillator is briefly discussed.

Bernard Yurke

A damped harmonic oscillator can be modeled as a manifestly conservative system by replacing the dissipative element with a string or transmission line of infinite extent. This conservative system can be quantized in a straightforward manner using the standard techniques of canonical quantization. The system may be used to illustrate various aspects of the quantum mechanics of a particle interacting with a field.