Path integral solution for some time-dependent potential

Christian Grosche

Ping Wang, Yang Xin-E, Song Xiao-Hui +1 more

Using coordinate-transformation we transformed a harmonic oscillator with time-d ependent mass and a time-dependent inverse potential into a harmonic oscillator with time-independent mass and a time-independent inverse potential accordingly. In terms of the relation between these two different harmonic oscillators' prop agators we derived the exact wavefunction of the former by Feynman path-integral . We also discussed the harmonic oscillator with more additional potentials.

Sergio A Albeverio, Sonia Mazzucchi

Christian Grosche

M. A. Kayed, Akira Inomata

An exact path-integral solution of the Dirac equation with a Coulomb potential is found. The energy-dependent Green's function of the second-order Dirac-Coulomb equation, expressed as a polar-coordinate path integral, is reduced to the exactly solvable path integral for an isotropic harmonic oscillator by a coordinate transformation combined with a local time rescaling. The Green's function of the linear Dirac equation is evaluated with the help of the Biedenharn transformation. The energy spectrum for the bound states is also obtained.

Liang Cai, Ping Zhang, Tao Yang +1 more

By using the path integral approach, we investigate the problem of Hooke's atom (two electrons interacting with Coulomb potential in an external harmonic-oscillator potential) in an arbitrary time-dependent electric field. For a certain infinite set of discrete oscillator frequencies, we obtain the analytical solutions. The ground state polarization of the atom is then calculated. The same result is also obtained through linear response theory.