Quantum propagator and characteristic equation in the presence of a chain of $\delta$-potentials

Abstract

The quantum propagator and characteristic equation in the presence of a chain of $\delta$-potentials are obtained in the rectangular, cylindrical and spherical coordinate systems. The simplicity and efficiency of the method is illustrated via examples. As an application, the characteristic equation of a quantum harmonic oscillator confined to an infinite box is obtained. The roots of the characteristic equation, determining the energy eigenvalues of the restricted oscillator, are calculated approximately and compared with the existing numerical data.

15 pages, 2 figures

References in corpus (7)

• Casimir Energies and Pressures for $\delta$-function Potentials
• Periodic integrable systems with delta-potentials
• Two-dimensional electron gas in a uniform magnetic field in the presence of a delta-impurity
• Particle in a box with a delta-function potential: strong and weak coupling limits
• Perturbative and non-perturbative studies with the delta function potential
• Exact propagators for atom-laser interactions
• Equation of state for the one-dimensional attractive δ-potential Bose gas in the weak-coupling regime