Interbasis expansions for isotropic harmonic oscillator

Shi Hai Dong

doi:10.1016/j.physleta.2012.02.042

Interbasis expansions for isotropic harmonic oscillator

Shi Hai Dong

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

3 Scopus citations

Abstract

The exact solutions of the isotropic harmonic oscillator are reviewed in Cartesian, cylindrical polar and spherical coordinates. The problem of interbasis expansions of the eigenfunctions is solved completely. The explicit expansion coefficients of the basis for given coordinates in terms of other two coordinates are presented for lower excited states. Such a property is occurred only for those degenerated states for given principal quantum number n.

Original language	English
Pages (from-to)	1262-1268
Number of pages	7
Journal	Physics Letters, Section A: General, Atomic and Solid State Physics
Volume	376
Issue number	15
DOIs	https://doi.org/10.1016/j.physleta.2012.02.042
State	Published - 12 Mar 2012

Keywords

Interbasis expansions
Isotropic harmonic oscillator
Schrödinger equation

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10.1016/j.physleta.2012.02.042

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title = "Interbasis expansions for isotropic harmonic oscillator",

abstract = "The exact solutions of the isotropic harmonic oscillator are reviewed in Cartesian, cylindrical polar and spherical coordinates. The problem of interbasis expansions of the eigenfunctions is solved completely. The explicit expansion coefficients of the basis for given coordinates in terms of other two coordinates are presented for lower excited states. Such a property is occurred only for those degenerated states for given principal quantum number n.",

keywords = "Interbasis expansions, Isotropic harmonic oscillator, Schr{\"o}dinger equation",

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doi = "10.1016/j.physleta.2012.02.042",

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T1 - Interbasis expansions for isotropic harmonic oscillator

AU - Dong, Shi Hai

PY - 2012/3/12

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N2 - The exact solutions of the isotropic harmonic oscillator are reviewed in Cartesian, cylindrical polar and spherical coordinates. The problem of interbasis expansions of the eigenfunctions is solved completely. The explicit expansion coefficients of the basis for given coordinates in terms of other two coordinates are presented for lower excited states. Such a property is occurred only for those degenerated states for given principal quantum number n.

AB - The exact solutions of the isotropic harmonic oscillator are reviewed in Cartesian, cylindrical polar and spherical coordinates. The problem of interbasis expansions of the eigenfunctions is solved completely. The explicit expansion coefficients of the basis for given coordinates in terms of other two coordinates are presented for lower excited states. Such a property is occurred only for those degenerated states for given principal quantum number n.

KW - Interbasis expansions

KW - Isotropic harmonic oscillator

KW - Schrödinger equation

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U2 - 10.1016/j.physleta.2012.02.042

DO - 10.1016/j.physleta.2012.02.042

M3 - Artículo

SN - 0375-9601

VL - 376

SP - 1262

EP - 1268

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

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

IS - 15

ER -

Interbasis expansions for isotropic harmonic oscillator

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Keywords

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