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Exactly solvable effective mass Schrödinger equation with coulomb‐like potential
Author(s) -
PachecoGarcía C.,
GarcíaRavelo J.,
Morales J.,
Peña J. J.
Publication year - 2010
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.22898
Subject(s) - schrödinger equation , physics , effective mass (spring–mass system) , eigenvalues and eigenvectors , position (finance) , morse potential , transformation (genetics) , canonical transformation , coulomb , quantum mechanics , constant (computer programming) , mathematical physics , quantum , chemistry , biochemistry , finance , computer science , economics , gene , programming language , electron
Abstract Exactly solvable Schrödinger equation (SE) with a position‐dependent mass distribution allowing Morse‐like eigenvalues is presented. For this, the position‐dependent mass Schrödinger equation is transformed into a standard SE, with constant mass, by means of the point canonical transformation scheme. In that method, the choice of potential for the position‐dependent mass Schrödinger equation allows us to obtain the transformation that should be used to find the exactly solvable SE. As a useful application of the proposal, the equivalent of the Witten superpotential is chosen to be constant to find the position‐dependent mass distribution and the exactly solvable potential V ( m ( x )) allowing Morse‐type energy spectra. This V ( m ( x )) is shown to have a Coulomb potential structure and can be useful in the study of the electronic properties of materials in which the carrier effective mass depends on the position. Moreover, the worked example, the approach is general and can be applied in the search of new potentials suitable on the study of quantum chemical systems. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2010