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Lagrangian form of Schrödinger equation

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Abstract

Lagrangian formulation of quantum mechanical Schrödinger equation is developed in general and illustrated in the eigenbasis of the Hamiltonian and in the coordinate representation. The Lagrangian formulation of physically plausible quantum system results in a well defined second order equation on a real vector space. The Klein–Gordon equation for a real field is shown to be the Lagrangian form of the corresponding Schrödinger equation.

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Acknowledgments

This work was supported in part by the Ministry of Education and Science of the Republic of Serbia, under project No. 171017, 171028 and 171006. and by COST (Action MP1006).

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Authors and Affiliations

  1. Institute of Physics, University of Belgrade, PO Box 68, 11000 , Belgrade, Serbia

    D. Arsenović, N. Burić & S. Prvanović

  2. Vinca Institute of Nuclear Sciences, University of Belgrade, Belgrade, Serbia

    D. M. Davidović

Authors
  1. D. Arsenović
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  2. N. Burić
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  3. D. M. Davidović
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  4. S. Prvanović
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Correspondence to N. Burić.

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Arsenović, D., Burić, N., Davidović, D.M. et al. Lagrangian form of Schrödinger equation. Found Phys 44, 725–735 (2014). https://doi.org/10.1007/s10701-014-9810-4

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  • DOI: https://doi.org/10.1007/s10701-014-9810-4

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