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We employ the point canonical transformation (PCT) to solve the D-dimensional Schr{o}dinger equation with position-dependent effective mass (PDEM) function for two molecular pseudoharmonic and modified Kratzer (Mie-type) potentials. In mapping the transformed exactly solvable D-dimensional ($Dgeq 2$) Schr{o}dinger equation with constant mass into the effective mass equation by employing a proper transformation, the exact bound state solutions including the energy eigenvalues and corresponding wave functions are derived. The well-known pseudoharmonic and modified Kratzer exact eigenstates of various dimensionality is manifested.
We study in detail the relationship between the Tavis-Cummings Hamiltonian of quantum optics and a family of quasi-exactly solvable Schrodinger equations. The connection between them is stablished through the biconfluent Heun equation. We found that
Exact solutions of effective radial Schr{o}dinger equation are obtained for some inverse potentials by using the point canonical transformation. The energy eigenvalues and the corresponding wave functions are calculated by using a set of mass distributions
A general form of the effective mass Schrodinger equation is solved exactly for Hulthen potential. Nikiforov-Uvarov method is used to obtain energy eigenvalues and the corresponding wave functions. A free parameter is used in the transformation of the wave function.
The three-dimensional Schrodinger equation with a position-dependent (effective) mass is studied in the framework of Supersymmetrical (SUSY) Quantum Mechanics. The general solution of SUSY intertwining relations with first order supercharges is obtai
We present the exact solution of the Klein-Gordon equation in D-dimensions in the presence of the noncentral equal scalar and vector pseudoharmonic potential plus the new ring-shaped potential using the Nikiforov-Uvarov method. We obtain the exact bo