Abstract
Exactly Solvable Potentials (ESPs) of Position-Dependent Mass (PDM) Schrodinger equation are generated from Hulthen Potential (parent system) by using Extended Transformation (ET) method. The method includes a Co-ordinate Transformation (CT) followed by Functional Transformation (FT) of wave function. Mass function of parent system gets transformed to that of generated system. Two new ESPs are generated. The explicit expressions of mass functions, energy eigenvalues and corresponding wave functions for newly generated potentials (systems) are derived. System specific regrouping method is also discussed.
Highlights
There are many physical examples of quantum mechanical problems in which Position-Dependent Mass (PDM) makes its appearance and leads to effective interactions giving interesting results
We have considered a real quantum mechanical potential VA(x), which is termed as A-quantum system (A-Quantum System (QS)). 1D-PDM Schrodinger equation for A-QS is
Since mass depends on position, we introduce transformation of mass i.e. mA(x) of A-QS transforms to new mass function mB(x) of B-QS, as given below mB x mA gB x
Summary
There are many physical examples of quantum mechanical problems in which Position-Dependent Mass (PDM) makes its appearance and leads to effective interactions giving interesting results. Special application of principal concept of PDM is found in the investigation of electronic properties of semiconductors [1], quantum dots and quantum wells [2, 3], quantum liquids [4], Nuclear many body problems[5] etc In these cases, Exact Analytic Solution (EAS) of PDM Schrödinger equation for a physical potential provides maximum information of the system. There has been a sustained effort in calculating EAS of PDM Schrödinger equation providing us with energy eigenvalues and corresponding eigenfunctions for physical potentials. Such studies use different methods known for solving constant mass Schrödinger equations or an extension of them.
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