Abstract
Within the framework of the translation operator for a quantum system with position-dependent mass, we examine the quantum state of a position-dependent mass system in a variable potential. By imposing conditions of resolvability, we arrive at a potential with a quartic and a quadratic term. It emerges naturally that the energy eigen states of the system are negative. We have found the quantum mechanical quantities: energy spectrum, eigen functions and uncertainty relation. These quantities depend on the parameters of the potential.
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