This book describes the Hamilton-Jacobi formalism of quantum mechanics, which allows

computation of eigenvalues of quantum mechanical potential problems without solving for the

wave function. The examples presented include exotic potentials such as quasi-exactly solvable models and Lame an dassociated Lame potentials. A careful application of boundary conditions offers an insight into the nature of solutions of several potential models. Advanced

undergraduates having knowledge of complex variables and quantum mechanics will find this

as an interesting method to obtain the eigenvalues and eigen-functions. The discussion on

complex zeros of the wave function gives intriguing new results which are relevant for

advanced students and young researchers. Moreover, a few open problems in research are

discussed as well, which pose a challenge to the mathematically oriented readers.