Heun functions and quasi-exactly solvable double-well potentials

We investigate a type of one-dimensional quasi-exactly solvable double-well potential whose analytical solution can be constructed in terms of the Heun functions. It is shown that for certain special values of the potential parameters, two energy eigenvalues and eigenstates of the lowest part of the...

Full description

Saved in:
Bibliographic Details
Published inJournal of physics. A, Mathematical and theoretical Vol. 46; no. 3; pp. 35301 - 9
Main Authors Chen, Bei-Hua, Wu, Yan, Xie, Qiong-Tao
Format Journal Article
LanguageEnglish
Published IOP Publishing 25.01.2013
Subjects
Construction
Eigenvalues
Functions (mathematics)
Mathematical analysis
Tunnelling
Online AccessGet full text

Cover

More Information
Summary:We investigate a type of one-dimensional quasi-exactly solvable double-well potential whose analytical solution can be constructed in terms of the Heun functions. It is shown that for certain special values of the potential parameters, two energy eigenvalues and eigenstates of the lowest part of the energy spectrum can be found exactly in explicit form. In addition, the Wronskian method has been applied to derive the conditions for the energy eigenvalues of the bound states. Our analytical results may find applications in the tunnelling problem for the double-well potentials.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8113/46/3/035301