Regular Article

The European Physical Journal D

, 66:22

First online:

Alternative analysis to perturbation theory in quantum mechanics

Dyson series in matrix form
  • J. Martínez-CarranzaAffiliated withInstituto Nacional de Astrofisica, Optica y Electronica
  • , F. Soto-EguibarAffiliated withInstituto Nacional de Astrofisica, Optica y Electronica
  • , H. Moya-CessaAffiliated withInstituto Nacional de Astrofisica, Optica y Electronica Email author 

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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.

Keywords

Quantum Optics