Eur. Phys. J. D (2012) 66: 22
https://doi.org/10.1140/epjd/e2011-20654-5

Regular Article

Alternative analysis to perturbation theory in quantum mechanics

Dyson series in matrix form

Instituto Nacional de Astrofisica, Optica y Electronica, Apartado Postal 51 y 216, 72000 Puebla, Pue., Mexico

^a e-mail: hmmc@inaoep.mx

Received: 10 November 2011
Published online: 31 January 2012

Abstract

We develop an alternative approach to the time independent perturbation theory in non-relativistic quantum mechanics. The method developed has the advantage to provide in one operation the correction to the energy and to the wave function; additionally we can analyze the time evolution of the system for any initial condition, which may be bothersome in the standard method. To verify our results, we apply our method to the harmonic oscillator perturbed by a quadratic potential. An alternative form of the Dyson series, in matrix form instead of integral form, is also obtained.