Exact solutions for time-dependent phenomena in quantum mechanics

John G. Hartley

Kálmán Varga, Joseph A. Driscoll

César Augusto Dartora, G. G. Cabrera, Kleber Zuza Nobrega

We introduce a modified version of the interaction picture applicable to situations in which the nonperturbed Hamiltonian is time-dependent but can be diagonalized by the same basis of states at all times. We probe the method using a simple model Hamiltonian to study the spin dynamics of molecular magnets with time-dependent fields. Fully quantum mechanical calculations show the superiority of our method compared to the usual time-dependent perturbation theory. Our approach takes into account time-dependent fields and converges rapidly to the exact solution.

Junhao, Z.

Quantum mechanics take the sum of first finite order approximate solutions of time-dependent perturbation to substitute the exact solution. From the point of mathematics, it may be correct only in the convergent region of the time-dependent perturbation series. Where is the convergent region of this series? Quantum mechanics did not answer this problem. However it is relative to the question, can we use the Schrodinger equation to describe the transition processes? So it is the most important unsettling problem of physical theory. We find out the time-dependent approximate solution for arbitrary and the exact solution. Then we can prove that: (1) In the neighborhood of the conservation of energy, the series is divergent. The basic error of quantum mechanics is using the sum of the first finite orders approximate solutions to substitute the exact solution in this divergent region. It leads to an infinite error. So the Fermi golden rule is not a mathematically reasonable inference of the. Schrodinger equation (2) The transiton probability per unit time deduced from the exact solution of Schrodinger equation cannot describe the transition processes. This paper is only a prime discussion.

Rafael Almeida, Daniel A. Morales

Exact analytical solutions are found for the quantum mechanical problem of a particle subject to a time-dependent potential with time-dependent boundary conditions. The method of solution employs time-dependent invariants, rescaling of space and time variables along with an unitary transformation. Several applications are discussed. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 827–833, 1997