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
Received: 10 November 2011
Published online: 31 January 2012
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.
Key words: Quantum Optics
© EDP Sciences, Società Italiana di Fisica and Springer-Verlag 2012