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Abstract
The position-dependent effective mass Schrödinger equation exhibiting a similar position dependence for both the potential and mass is exactly solved. Some physical examples are given for bound and scattering systems. We analyze the behavior of the wavefunctions for scattered states in light of the parameters involved. We show that the parameters of the potential play a crucial role.
Highlights
Systems that involve a position-dependent effective mass (PDEM) are represented by a Hamiltonian composed of kinetic energy and potential energy operators H = Ek + V
We have studied the PDEM Schrödinger equation for similar position dependence of potential and mass
We have studied some physical examples and calculated for the bound states the energy eigenvalues for mass m = m0/(az + b)[2] and we have discussed the behavior of the wavefunction for the exponential, hyperbolic tangent, and q-deformed secant hyperbolic potentials
Summary
The physical description of quantum systems is encapsulated in the Schrödinger equation. To explore the physics of the quantum system, we need to solve that equation. Systems that involve a PDEM are represented by a Hamiltonian composed of kinetic energy and potential energy operators H = Ek + V. The generalized form of the kinetic energy operator for the PDEM model as suggested by O. von Roos[22] is given by.
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