### Abstract

The solution of the one-dimensional Schrödinger equation is discussed in the case of position-dependent mass. The general formalism is specified for potentials that are solvable in terms of generalized Laguerre polynomials and mass functions that are positive and bounded on the whole real x axis. The resulting four-parameter potential is shown to belong to the class of "implicit" potentials. Closed expressions are obtained for the bound-state energies and the corresponding wave functions, including their normalization constants. The constant mass case is obtained by a specific choice of the parameters. It is shown that this potential contains both the harmonic oscillator and the Morse potentials as two distinct limiting cases and that the original potential carries several characteristics of these two potentials. Possible generalizations of the method are outlined.

Original language | English |
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Article number | 092103 |

Journal | Journal of Mathematical Physics |

Volume | 51 |

Issue number | 9 |

DOIs | |

Publication status | Published - Sep 2010 |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Journal of Mathematical Physics*,

*51*(9), [092103]. https://doi.org/10.1063/1.3483716

**An exactly solvable Schrödinger equation with finite positive position-dependent effective mass.** / Lévai, G.; Özer, O.

Research output: Contribution to journal › Article

*Journal of Mathematical Physics*, vol. 51, no. 9, 092103. https://doi.org/10.1063/1.3483716

}

TY - JOUR

T1 - An exactly solvable Schrödinger equation with finite positive position-dependent effective mass

AU - Lévai, G.

AU - Özer, O.

PY - 2010/9

Y1 - 2010/9

N2 - The solution of the one-dimensional Schrödinger equation is discussed in the case of position-dependent mass. The general formalism is specified for potentials that are solvable in terms of generalized Laguerre polynomials and mass functions that are positive and bounded on the whole real x axis. The resulting four-parameter potential is shown to belong to the class of "implicit" potentials. Closed expressions are obtained for the bound-state energies and the corresponding wave functions, including their normalization constants. The constant mass case is obtained by a specific choice of the parameters. It is shown that this potential contains both the harmonic oscillator and the Morse potentials as two distinct limiting cases and that the original potential carries several characteristics of these two potentials. Possible generalizations of the method are outlined.

AB - The solution of the one-dimensional Schrödinger equation is discussed in the case of position-dependent mass. The general formalism is specified for potentials that are solvable in terms of generalized Laguerre polynomials and mass functions that are positive and bounded on the whole real x axis. The resulting four-parameter potential is shown to belong to the class of "implicit" potentials. Closed expressions are obtained for the bound-state energies and the corresponding wave functions, including their normalization constants. The constant mass case is obtained by a specific choice of the parameters. It is shown that this potential contains both the harmonic oscillator and the Morse potentials as two distinct limiting cases and that the original potential carries several characteristics of these two potentials. Possible generalizations of the method are outlined.

UR - http://www.scopus.com/inward/record.url?scp=78049425860&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78049425860&partnerID=8YFLogxK

U2 - 10.1063/1.3483716

DO - 10.1063/1.3483716

M3 - Article

AN - SCOPUS:78049425860

VL - 51

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 9

M1 - 092103

ER -