Position-Dependent Mass and the Extended Uncertainty Principle Applications: Path Integral Technique
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Description
Using the Feynman path integral formulation, we treated some problems of relativistic and nonrelativistic quantum mechanics in the context of position-dependent mass (PDM) and the extended uncertainty principle (EUP): In the first part of the first section, the general form of propagator for position-dependent mass (PDM) systems based on the generalized translation operator in the position space representation in one dimension is found. As special cases, the energy eigenvalues and their corresponding eigenfunctions for the harmonic oscillator, exponential and Mathews-Lakshmanan oscillator potentials are extracted. In the absence of PDM, the usual resutls are recovered. In the second part of the same section, we generalized the Feynman path integral formalism for PDM systems to D-dimensions.