9 research outputs found
On Exactness Of The Supersymmetric WKB Approximation Scheme
Exactness of the lowest order supersymmetric WKB (SWKB) quantization
condition , for certain
potentials, is examined, using complex integration technique. Comparison of the
above scheme with a similar, but {\it exact} quantization condition, , originating from the quantum Hamilton-Jacobi
formalism reveals that, the locations and the residues of the poles that
contribute to these integrals match identically, for both of these cases. As
these poles completely determine the eigenvalues in these two cases, the
exactness of the SWKB for these potentials is accounted for. Three non-exact
cases are also analysed; the origin of this non-exactness is shown to be due
the presence of additional singularities in , like branch
cuts in the plane.Comment: 11 pages, latex, 1 figure available on reques
The Generalized PT-Symmetric Sinh-Gordon Potential Solvable within Quantum Hamilton-Jacobi Formalism
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.Comment: 10 pages appear to in IJT