Hermitian and gauge-covariant Hamiltonians for a particle in a magnetic field on cylindrical and spherical surfaces

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2017-01-01

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Shikakhwa, M. S.
Chair, N.

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We construct the Hermitian Schrodinger Hamiltonian of spin-less particles and the gauge-covariant Pauli Hamiltonian of spin one-half particles in a magnetic field, which are confined to cylindrical and spherical surfaces. The approach does not require the use of involved differential-geometrical methods and is intuitive and physical, relying on the general requirements of Hermicity and gauge-covariance. The surfaces are embedded in the full three-dimensional space and confinement to the surfaces is achieved by strong radial potentials. We identify the Hermitian and gauge-covariant (in the presence of a magnetic field) physical radial momentum in each case and set it to zero upon confinement to the surfaces. The resulting surface Hamiltonians are seen to be automatically Hermitian and gauge-covariant. The well-known geometrical kinetic energy also emerges naturally.

Subject Keywords

General Physics and Astronomy

URI

https://hdl.handle.net/11511/65122

Journal

EUROPEAN JOURNAL OF PHYSICS

DOI

https://doi.org/10.1088/0143-0807/38/1/015402

Collections

Natural Sciences and Mathematics, Article

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Citation Formats

M. S. Shikakhwa and N. Chair, “Hermitian and gauge-covariant Hamiltonians for a particle in a magnetic field on cylindrical and spherical surfaces,” EUROPEAN JOURNAL OF PHYSICS, pp. 0–0, 2017, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/65122.