Quasiexactly solvable problems in the path-integral formalism

Quasiexactly solvable problems are treated via the path-integral approach. The generalized Duru-Kleinert formalism involving a combination of a point-canonical transformation and a new-time transformation is applied to power-law and Morse-like quasiexactly solvable problems, and it is shown that these can be grouped into two families. A truncated kernel hypothesis is advanced, whereby the exactly solvable parts of the kernels of each problem within a given family can be transformed into one another. As an application, the ground-state energy eigenvalue and wave function of the N=0 generalized harmonic oscillator are derived from those of the N=0 generalized Coulomb problem.