The Feynman path integral representation for the weak solution of the Schrödinger equation with an inverse quartic oscillator potential is given in terms of a well defined infinite dimensional oscillatory integral. An analytically continued Wiener integral representation for the solution is provided and an explicit description of the quantum dynamics associated with a nonessentially self-adjoint Hamiltonian is given.

Journal of Mathematical PhysicsSep 1, 20089 citations

Path Integral Evaluation of a Time-Dependent Oscillator in an External Field

A. N. Ikot, Eno E. Ituen, Ime. E. Essien +1 more

The Lagrangian of a system describing the dynamical behaviour of a time-dependent harmonic oscillator is modified and then used to evaluate the Feynman path integral of the oscillator. The path integral of the time-dependent oscillator is shown to reduce to the time-independent within certain limits.

TURKISH JOURNAL OF PHYSICSNov 26, 20084 citations