Exact solutions and ladder operators for a new anharmonic oscillator

Shi Hai Dong; Guo Hua Sun; M. Lozada-Cassou

doi:10.1016/j.physleta.2005.04.024

Exact solutions and ladder operators for a new anharmonic oscillator

Shi Hai Dong, Guo Hua Sun, M. Lozada-Cassou

Research output: Contribution to journal › Article › peer-review

50 Scopus citations

Abstract

In this Letter, we propose a new anharmonic oscillator and present the exact solutions of the Schrödinger equation with this oscillator. The ladder operators are established directly from the normalized radial wave functions and used to evaluate the closed expressions of matrix elements for some related functions. Some comments are made on the general calculation formula and recurrence relation for off-diagonal matrix elements. Finally, we show that this anharmonic oscillator possesses a hidden symmetry between E(r) and E(ir) by substituting r→ir.

Original language	English
Pages (from-to)	94-103
Number of pages	10
Journal	Physics Letters, Section A: General, Atomic and Solid State Physics
Volume	340
Issue number	1-4
DOIs	https://doi.org/10.1016/j.physleta.2005.04.024
State	Published - 6 Jun 2005
Externally published	Yes

Keywords

Anharmonic oscillator
Exact solutions
Ladder operators

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10.1016/j.physleta.2005.04.024

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title = "Exact solutions and ladder operators for a new anharmonic oscillator",

abstract = "In this Letter, we propose a new anharmonic oscillator and present the exact solutions of the Schr{\"o}dinger equation with this oscillator. The ladder operators are established directly from the normalized radial wave functions and used to evaluate the closed expressions of matrix elements for some related functions. Some comments are made on the general calculation formula and recurrence relation for off-diagonal matrix elements. Finally, we show that this anharmonic oscillator possesses a hidden symmetry between E(r) and E(ir) by substituting r→ir.",

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author = "Dong, {Shi Hai} and Sun, {Guo Hua} and M. Lozada-Cassou",

note = "Funding Information: This work is partially supported by IMP. The authors would like to thank the kind referee for the positive and invaluable suggestions, from which the manuscript has been improved greatly.",

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T1 - Exact solutions and ladder operators for a new anharmonic oscillator

AU - Dong, Shi Hai

AU - Sun, Guo Hua

AU - Lozada-Cassou, M.

N1 - Funding Information: This work is partially supported by IMP. The authors would like to thank the kind referee for the positive and invaluable suggestions, from which the manuscript has been improved greatly.

PY - 2005/6/6

Y1 - 2005/6/6

N2 - In this Letter, we propose a new anharmonic oscillator and present the exact solutions of the Schrödinger equation with this oscillator. The ladder operators are established directly from the normalized radial wave functions and used to evaluate the closed expressions of matrix elements for some related functions. Some comments are made on the general calculation formula and recurrence relation for off-diagonal matrix elements. Finally, we show that this anharmonic oscillator possesses a hidden symmetry between E(r) and E(ir) by substituting r→ir.

AB - In this Letter, we propose a new anharmonic oscillator and present the exact solutions of the Schrödinger equation with this oscillator. The ladder operators are established directly from the normalized radial wave functions and used to evaluate the closed expressions of matrix elements for some related functions. Some comments are made on the general calculation formula and recurrence relation for off-diagonal matrix elements. Finally, we show that this anharmonic oscillator possesses a hidden symmetry between E(r) and E(ir) by substituting r→ir.

KW - Anharmonic oscillator

KW - Exact solutions

KW - Ladder operators

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DO - 10.1016/j.physleta.2005.04.024

M3 - Artículo

SN - 0375-9601

VL - 340

SP - 94

EP - 103

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

IS - 1-4

ER -

Exact solutions and ladder operators for a new anharmonic oscillator

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Keywords

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