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The generalized \(PT\) -symmetric sinh-gordon potential solvable within quantum Hamilton-Jacobi formalism. (English) Zbl 1139.81344

Summary: The generalized Sinh-Gordon potential is solved within quantum Hamiltonian Jacobi approach in the framework of \(PT\) symmetry. The quasi exact solutions of energy eigenvalues and eigenfunctions of the generalized Sinh-Gordon potential are found for \(n=0,1\) states.

MSC:

81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
35Q55 NLS equations (nonlinear Schrödinger equations)
70H20 Hamilton-Jacobi equations in mechanics
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