Abstract
We study the Schrödinger equation with a new quasi-exactly solvable double-well potential. Exact expressions for the energies, the corresponding wave functions, and the allowed values of the potential parameters are obtained using two different methods, the Bethe ansatz method and the Lie algebraic approach. Some numerical results are reported and it is shown that the results are in good agreement with each other and with those obtained previously via a different method.
Highlights
A quantum mechanical system is exactly solvable (ES) if all the eigenvalues and corresponding eigenfunctions can be determined exactly through algebraic means
On the other hand, during the last decades, a great deal of attention has been given to the study of the Schrodinger equation with quasi-exactly solvable (QES) double-well potential (DWP) including the quartic potential [22], the sextic potential [23], and the Razavy potential [24]
In this paper, applying the analytical approach of quasi-exact solvability, we investigate the Schrodinger equation for a new type of one-dimensional QES DWP proposed by Chen et al [17]
Summary
A quantum mechanical system is exactly solvable (ES) if all the eigenvalues and corresponding eigenfunctions can be determined exactly through algebraic means. In this paper, applying the analytical approach of quasi-exact solvability, we investigate the Schrodinger equation for a new type of one-dimensional QES DWP proposed by Chen et al [17]. They studied the problem and obtained solutions of the first two states by using two methods, the confluent Heun functions and the Wronskian method [17].
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
