A note on dirac's time-dependent perturbation theory

I-Tung Wang, Ta‐You Wu

Namita Gupta

S. C. Mehrotra, James E. Boggs

A time-dependent perturbation theory for the solution of the time-dependent Schrödinger equation is developed and is applied to systems having two states with pulse and Lorentzian types of perturbations. It is shown in the case of the pulse perturbation that the expression corresponding to the Nth order of the perturbation theory converges to the exact solution when N tends to infinity. The results obtained from this perturbation theory, the Magnus approximation, and the time-dependent perturbation theory developed by Dirac are compared with the exact results. This theory is found to be good for larger values of the perturbations and for larger intervals of time.

S. Rajasekar, R. Velusamy

Approximation methods are developed for systems where the time dependence of the Hamiltonian is small, slowly varying or rapidly varying. These correspond to perturbation, adiabatic and sudden approximations respectively. In this chapter we consider the time-dependent perturbation theory applicable for small time-dependent perturbation. This is the case when we wish to investigate the response of systems to incident radiation. The incident electromagnetic wave makes the electric and magnetic potentials to oscillate and the perturbation is usually very small compared with the static Hamiltonian. The theory of time-dependent perturbation was developed by Dirac in 1927 [1]. In this chapter we discuss the theory for constant and harmonic perturbations applied during a finite time interval, adiabatic and sudden perturbations.

K.C. Kar

Khinlay Win, A. Petridis