Free One-Dimensional Particle on an Interval

  • D. M. Gitman
  • I. V. Tyutin
  • B. L. Voronov
Part of the Progress in Mathematical Physics book series (PMP, volume 62)


Based on the general considerations in the previous Chapters, we consider the self-adjoint extension and spectral problems for the momentum and Hamiltonian of a free one-dimensional nonrelativistic particle moving on an interval of the real axis. The solution of these problems crucially depends on the type of the interval. It is shown how the correct treatment removes all the paradoxes presented in the Introduction.


Free Particle Momentum Operator Inversion Formula Finite Interval Boundary Form 
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  1. 77.
    Gitman, D.M., Tyutin, I.V., Voronov, B.L.: Oscillator representations for self-adjoint Calogero Hamiltonians. Journ. Phys. A Math. Theor. 44 425204 (2011)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • D. M. Gitman
    • 1
  • I. V. Tyutin
    • 2
  • B. L. Voronov
    • 2
  1. 1.Instituto de FísicaUniversidade de São PauloSão PauloBrasil
  2. 2.Department of Theoretical PhysicsP.N. Lebedev Physical InstituteMoscowRussia

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