Heun functions and quasi-exactly solvable double-well potentials

• Published in: Journal 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
• Language: English
• Published: IOP Publishing 25.01.2013
• Subjects: Construction; Eigenvalues; Functions (mathematics); Mathematical analysis; Tunnelling

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...