Conditionally exactly solvable singular even power potential in supersymmetric quantum mechanics

We solve strongly singular even power potential with inverse quadratic, inverse quartic and inverse sextic terms, using superpotential ansatz technique. We show that our new technique is very powerful and simple compared to traditional wave function ansatz technique. We also point out conditional shape invariance as the underlying symmetry to get conditional exactness. We also generalize the case for two-body Hamiltonian and propose an alternative way to solve Riccati equation instead of solving Schrodinger equation. We present operator formalism which is rather powerful. We also discuss the problem encountered in generalizing the potential for an N-body system.