Position dependent mass quantum particle

ABSTRACT: In this thesis we study a quantum particle with position dependent mass (PDM). We start from the general form of the kinetic energy operator in which the physical requirements are considered and then we show that the general form of the kinetic energy operator does not keep the Schrodinger equation invariant under the global Galilean transformation. To make out the problem we introduce instantaneous Galilean invariance and following this concept we show that in some specific case of the general form of the kinetic operator the Schrodinger equation remains invariant under the Galilean transformation. Furthermore we study a specific mass for a particle in an infinite square well potential. We show that the particle prefers to stay in a region with larger mass. Keywords: Position dependent mass, Quantum particle, Galilean invariance, Instantaneous Galilean invariance, Particle in infinite well. …………………………………………………………………………………………………………………………………………………………………………………………………………