Bound states of oscillators in infinite and finite domains: A semiclassical study

Abstract

AbstractBy involving the uncertainty product along with a semiclassical requirement for observables, a simple variational scheme is employed to extract major features of bound states of systems in (−∞,∞) and the same of systems confined in (−L,L). Special attention is paid to perturbative studies on the asymptotic behavior of energies for oscillators in infinite domains and dependence of energy spectra of oscillators in finite domains on various system parameters. A corrected form of the virial theorem is obtained in the latter case. The governing equations for quantum isothermal and adiabatic processes, derived recently, are also shown to be modified for general confined oscillator systems and closed‐form expressions are found. These results are useful in dealing with the quantum Carnot cycles. Advantages of the present route over other semiclassical strategies are stressed. Pilot calculations demonstrate nicely the efficacy of the endeavor under various situations. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001