A quantum particle in a nonstationary Coulomb potential

Eun Ji Jang, Young Kyu Lee, Won Sang Chung

В. И. Высоцкий, STANISLAV V. ADAMENKO

Premises for the formation of a correlated coherent state of particles in nonstationary quantum systems are considered. The relation between the correlation factor of particles and the probability of their passage through the potential barrier (including that in nuclear reactions) is analyzed. The optimal regime for parametric excitation of a harmonic oscillator is found, in which the asymptotic formation of the correlated state of particles takes place, the dispersion of their coordinates increases manifold, and the barrier transparency becomes many orders of magnitude higher at a low energy of interacting particles.

Salah Menouar, Mustapha Maamache, Jeong Ryeol Choi +1 more

Exact solutions of the one-dimensional Schrödinger equation with a time-dependent Coulomb potential [- z ( t )/| x |] are investigated using the invariant method (Lewis and Riesenfeld theorem) together with unitary transformation approach. The eigenfunctions and the corresponding eigenvalues of the system are obtained analytically. When the time dependence of all coefficients vanishes, our results exactly reduce to those known for stationary case.

Valentin N. Ostrovsky

The nonstationary Schr\"odinger equation is considered in a finite basis of states. The model Hamiltonian matrix corresponds to a single diabatic potential curve with a Coulombic $\ensuremath{\sim}1/t$ time dependence. An arbitrary number of other diabatic potential curves are flat, i.e., time independent and have arbitrary energies. Related states are coupled by constant interactions with the Coulomb state. The resulting nonstationary Schr\"odinger equation is solved by the method of contour integral. Probabilities of transitions to any other state are obtained as $\stackrel{\ensuremath{\rightarrow}}{t}\ensuremath{\infty}$ in a simple analytical form for the case when the Coulomb state is populated initially (at instant of time $\stackrel{\ensuremath{\rightarrow}}{t}+0).$ The formulas apply both to the cases when a horizontal diabatic potential curve is crossed by the Coulomb one and to a noncrossing situation. In the limit of weak coupling, the transition probabilities are interpreted in terms of a sequence of pairwise Landau-Zener-type transitions. Mapping of the Coulomb model onto an exactly solvable exponential multistate model is established. For the special two-state case, the well-known Nikitin model is recovered.

M. A. Markov