Alternative analysis to perturbation theory in quantum mechanics

@article{MartinezCarranza2011AlternativeAT,
  title={Alternative analysis to perturbation theory in quantum mechanics},
  author={Juan Martinez-Carranza and Francisco Soto-Eguibar and H{\'e}ctor Manuel Moya-Cessa},
  journal={The European Physical Journal D},
  year={2011},
  volume={66},
  pages={1-6}
}
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… 

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References

SHOWING 1-10 OF 12 REFERENCES

Alternative quantum perturbation theory without divergences

A different integral form of the Schrodinger equation and some boundedness conditions of the wave functions are proved, which exhibit the origin of some divergences in quantum mechanics. The

A quick perturbative method for Schrödinger equations

Within the framework of perturbation theory we propose, firstly, an iterative method which may serve as a source of optimal unperturbed solutions in both one and more dimensions. It combines the

Boundedness and convergence of perturbed corrections for helium-like ions in ground states

Applying the improved Rayleigh–Schrodinger perturbation theory based on an integral equation to helium-like ions in ground states and treating electron correlations as perturbations, we obtain the

The Radiation Theories of Tomonaga, Schwinger, and Feynman

A unified development of the subject of quantum electrodynamics is outlined, embodying the main features both of the Tomonaga-Schwinger and of the Feynman radiation theory. The theory is carried to a

Cavity quantum electrodynamics : the strange theory of light in a box

Preface. Acknowledgments. 1. Introduction. 2. Fiat Lux! 3. The Photon's Wavefunction. 4. A Box of Photons. 5. Let Matter Be! 6. Spontaneous Emission. 7. Macroscopic QED. 8. The Maser, the Laser, and

Diatomic Molecules According to the Wave Mechanics. II. Vibrational Levels

An exact solution is obtained for the Schroedinger equation representing the motions of the nuclei in a diatomic molecule, when the potential energy function is assumed to be of a form similar to