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arXiv:1208.4628

The Ordering Ambiguity

S. Habib Mazharimousavi

Published Aug 22, 2012• 0 citations
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Abstract

The kinetic energy operator of a quantum particle with position dependent mass and the associated ordering ambiguity is revisited. We introduce a new form of this operator which is a continues or discreet superposition of the acceptable values for the ordering parameters.
DOI
10.48550/arxiv.1208.4628

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In this article, an analysis of the kinetic energy operator introduced by O. von Roos is performed. Such analysis allows for determining the energy of a particle when its mass is position-dependent within a specific medium. The work, focused on the discussion of this concept in quantum mechanics courses, reveals how to apply the operator to numerically solve the one-dimensional Schrödinger equation for an electron rigidly confined within a semiconductor structure having a specific width (considering that the particle is subject to the action of a position-dependent quadratic potential). The Schrödinger equation is solved considering the mass of the electron constant, allowing a comparison of the obtained energies for this case as well as the ones that correspond to the case involving a position-dependent mass and taking into consideration several values of the structure width where the particle is confined. Observations during the analysis reveal how the ambiguity of the parameters that appear in the von Roos operator leads us to conclude that several dynamic systems can be associated to a given form of the potential energy.