### Abstract

An algebraic method of constructing potentials for which the Schrödinger equation with position dependent mass can be solved exactly is presented. A general form of the generators of su(1,1) algebra has been employed with a unified approach to the problem. Our systematic approach reproduces a number of earlier results and also leads to some novelties. We show that the solutions of the Schrödinger equation with position dependent mass are free from the choice of parameters for position dependent mass. Two classes of potentials are constructed that include almost all exactly solvable potentials.

Original language | English |
---|---|

Pages (from-to) | 8105-8112 |

Number of pages | 8 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 36 |

Issue number | 29 |

DOIs | |

Publication status | Published - Jul 25 2003 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Journal of Physics A: Mathematical and General*,

*36*(29), 8105-8112. https://doi.org/10.1088/0305-4470/36/29/315

**A systematic study on the exact solution of the position dependent mass Schrödinger equation.** / Koç, Ramazan; Koca, Mehmet.

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and General*, vol. 36, no. 29, pp. 8105-8112. https://doi.org/10.1088/0305-4470/36/29/315

}

TY - JOUR

T1 - A systematic study on the exact solution of the position dependent mass Schrödinger equation

AU - Koç, Ramazan

AU - Koca, Mehmet

PY - 2003/7/25

Y1 - 2003/7/25

N2 - An algebraic method of constructing potentials for which the Schrödinger equation with position dependent mass can be solved exactly is presented. A general form of the generators of su(1,1) algebra has been employed with a unified approach to the problem. Our systematic approach reproduces a number of earlier results and also leads to some novelties. We show that the solutions of the Schrödinger equation with position dependent mass are free from the choice of parameters for position dependent mass. Two classes of potentials are constructed that include almost all exactly solvable potentials.

AB - An algebraic method of constructing potentials for which the Schrödinger equation with position dependent mass can be solved exactly is presented. A general form of the generators of su(1,1) algebra has been employed with a unified approach to the problem. Our systematic approach reproduces a number of earlier results and also leads to some novelties. We show that the solutions of the Schrödinger equation with position dependent mass are free from the choice of parameters for position dependent mass. Two classes of potentials are constructed that include almost all exactly solvable potentials.

UR - http://www.scopus.com/inward/record.url?scp=0042843392&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0042843392&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/36/29/315

DO - 10.1088/0305-4470/36/29/315

M3 - Article

VL - 36

SP - 8105

EP - 8112

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 29

ER -