Semi-exact solutions of sextic potential plus a centrifugal term

Qian Dong; Guo Hua Sun; Bing He; Shi Hai Dong

doi:10.1007/s10910-020-01169-4

Semi-exact solutions of sextic potential plus a centrifugal term

Qian Dong, Guo Hua Sun, Bing He, Shi Hai Dong

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

6 Scopus citations

Abstract

We revisit the one-dimensional quantum system of a sextic potential added with a centrifugal term, V(x)=ax-2+bx2+cx4+dx6, where the parameters a, b, c and d are arbitrary. We find that its solutions can be expressed as a Biconfluent Heun function H_B(α, β, γ, δ; z) , while the associated energy spectrum is determined by the parameter δ. The semi-exact solutions of wave functions fully consist with the properties of the potential.

Original language	English
Pages (from-to)	2197-2203
Number of pages	7
Journal	Journal of Mathematical Chemistry
Volume	58
Issue number	10
DOIs	https://doi.org/10.1007/s10910-020-01169-4
State	Published - 1 Nov 2020

Keywords

Biconfluent Heun function
Semi-exact solutions
Sextic potential

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10.1007/s10910-020-01169-4

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title = "Semi-exact solutions of sextic potential plus a centrifugal term",

abstract = "We revisit the one-dimensional quantum system of a sextic potential added with a centrifugal term, V(x)=ax-2+bx2+cx4+dx6, where the parameters a, b, c and d are arbitrary. We find that its solutions can be expressed as a Biconfluent Heun function HB(α, β, γ, δ; z) , while the associated energy spectrum is determined by the parameter δ. The semi-exact solutions of wave functions fully consist with the properties of the potential.",

keywords = "Biconfluent Heun function, Semi-exact solutions, Sextic potential",

author = "Qian Dong and Sun, {Guo Hua} and Bing He and Dong, {Shi Hai}",

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T1 - Semi-exact solutions of sextic potential plus a centrifugal term

AU - Dong, Qian

AU - Sun, Guo Hua

AU - He, Bing

AU - Dong, Shi Hai

PY - 2020/11/1

Y1 - 2020/11/1

N2 - We revisit the one-dimensional quantum system of a sextic potential added with a centrifugal term, V(x)=ax-2+bx2+cx4+dx6, where the parameters a, b, c and d are arbitrary. We find that its solutions can be expressed as a Biconfluent Heun function HB(α, β, γ, δ; z) , while the associated energy spectrum is determined by the parameter δ. The semi-exact solutions of wave functions fully consist with the properties of the potential.

AB - We revisit the one-dimensional quantum system of a sextic potential added with a centrifugal term, V(x)=ax-2+bx2+cx4+dx6, where the parameters a, b, c and d are arbitrary. We find that its solutions can be expressed as a Biconfluent Heun function HB(α, β, γ, δ; z) , while the associated energy spectrum is determined by the parameter δ. The semi-exact solutions of wave functions fully consist with the properties of the potential.

KW - Biconfluent Heun function

KW - Semi-exact solutions

KW - Sextic potential

UR - http://www.scopus.com/inward/record.url?scp=85091070248&partnerID=8YFLogxK

U2 - 10.1007/s10910-020-01169-4

DO - 10.1007/s10910-020-01169-4

M3 - Artículo

AN - SCOPUS:85091070248

SN - 0259-9791

VL - 58

SP - 2197

EP - 2203

JO - Journal of Mathematical Chemistry

JF - Journal of Mathematical Chemistry

IS - 10

ER -

Semi-exact solutions of sextic potential plus a centrifugal term

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Keywords

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