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Class of invariants for a time dependent linear potential

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Abstract

General solution of the one-dimensional Schrödinger equation in presence of a time-dependent linear potential is reconsidered in the context of Lewis–Riesenfeld and unitary transformation approaches. Three invariant operators are constructed as limiting cases of a general Hermitian quadratic invariant and their instantaneous eigenfunctions are obtained. Then the corresponding solutions of Schrödinger equation for each invariant operator are derived. These solutions include all known solutions of the system. Furthermore, it is shown how different solutions can be related to each other.

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Acknowledgments

This work was supported by MESRS and DGRSDT Algeria.

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Authors and Affiliations

  1. Laboratoire de Physique Théorique, Département de Physique, Faculté des Sciences Exactes, Université Constantine 1, 25000, Constantine, Algeria

    M. Berrehail & F. Benamira

  2. Département des Sciences de la matière, Université de Bordj Bou Arreridj, 43000, Bordj Bou Arreridj, Algeria

    M. Berrehail

Authors
  1. M. Berrehail
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  2. F. Benamira
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Correspondence to M. Berrehail.

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Berrehail, M., Benamira, F. Class of invariants for a time dependent linear potential. Indian J Phys 87, 1023–1027 (2013). https://doi.org/10.1007/s12648-013-0322-4

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  • DOI: https://doi.org/10.1007/s12648-013-0322-4

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