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 [(X) over cap, (N) over cap] = i (h) over bar (1 + beta($) over cap (2)), leading to the existence of a minimal observable length (h) over bar root beta. 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.