Analytical solution to position dependent mass Schro¨ dinger equation
Pankaj K. Jhaa
Yuri V. Rostovtsevc
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Using a recently developed technique to solve the Schro¨ dinger equation for constant mass, we have studied the regime in which the mass varies with position, i.e. the position-dependent mass Schro¨ dinger equation (PDMSE). We obtained an analytical solution for the PDMSE and applied our approach to study a position dependent mass m(x) particle scattered by a potentialVðxÞ. We have also studied the structural analogy between the PDMSE and the two-level atomic system interacting with a classical field.