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Quantum motion on two planes connected at one point

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Abstract

We study the free motion of a particle on the manifold which consists of two planes connected at one point. The four-parameter family of admissible Hamiltonians is constructed by self-adjoint extensions of the free Hamiltonian with the singular point removed. The probability of penetration between the two parts of the configuration manifold is calculated. The results can be used as a model for quantum point-contact spectroscopy.

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Author notes

  1. P. Exner

    Present address: Nuclear Physics Institute, Czechoslovak Academy of Sciences, 25068, Řež near Prague, Czechoslovakia

  2. P. Sěba

    Present address: Nuclear Centre, Charles University, V Holešovičkách 2, 18000, Prague, Czechoslovakia

Authors and Affiliations

  1. Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 141980, Dubna, U.S.S.R.

    P. Exner & P. Sěba

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  1. P. Exner
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  2. P. Sěba
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Exner, P., Sěba, P. Quantum motion on two planes connected at one point. Lett Math Phys 12, 193–198 (1986). https://doi.org/10.1007/BF00416509

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  • DOI: https://doi.org/10.1007/BF00416509

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