Path integral treatment of the one-dimensional Klein–Gordon oscillator with minimal length

Abstract

The path integral method is used to present an exact treatment of the one-dimensional Klein–Gordon oscillator in the context of quantum mechanics with a deformed Heisenberg algebra of the form , leading to the existence of a minimal observable length . We tackle the problem in the momentum space and we use the Schwinger proper-time method to represent Green's function. Calculations are run with the help of the point canonical transformation technique. The bound-state energy spectrum and the associated momentum space eigenfunctions are obtained, and a detailed comparison with the results for the undeformed case is made.