The European Physical Journal D

, 66:22

Alternative analysis to perturbation theory in quantum mechanics

Dyson series in matrix form


  • J. Martínez-Carranza
    • Instituto Nacional de AstrofisicaOptica y Electronica
  • F. Soto-Eguibar
    • Instituto Nacional de AstrofisicaOptica y Electronica
    • Instituto Nacional de AstrofisicaOptica y Electronica
Regular Article

DOI: 10.1140/epjd/e2011-20654-5

Cite this article as:
Martínez-Carranza, J., Soto-Eguibar, F. & Moya-Cessa, H. Eur. Phys. J. D (2012) 66: 22. doi:10.1140/epjd/e2011-20654-5


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.


Quantum Optics

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© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2012