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Exact Solutions to Schrödinger Equation for a Charged Particle on a Torus in Uniform Electric and Magnetic Fields

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Abstract

We present exact solutions of the Schrödinger equation for a charged particle constrained to move along a toroidal surface in the presence of uniform electric and magnetic fields.

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Funding

The author received partial financial support from FAPERJ.

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Authors and Affiliations

  1. Departamento de Física de Volta Redonda, Instituto de Ciências Exatas — Universidade Federal Fluminense, R. Des. Ellis Hermydio Figueira, 783, Bloco C, Volta Redonda RJ, CEP 27213-415, Brazil

    Alexandre G. M. Schmidt

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Correspondence to Alexandre G. M. Schmidt.

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Appendix A: Fourier coefficients

Appendix A: Fourier coefficients

Our paper’s workhorse is the ansatz (14) which we used to solve Hill’s equation as well as a more general one involving not only cosines but also sines. For each value of angular momentum m we have a different set of coefficients bn. In this Appendix we present the most important coefficients of several eigenfunctions for the three problems we studied: free charged particle; charge interacting with a uniform magnetic field; and charge interacting with a uniform electric field.

Table 2 First seven Fourier coefficients for u(z) given by (14)—torus without fields
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Table 3 First seven Fourier coefficients for u(z) given by (14)—torus with magnetic field
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Table 4 Seven Fourier coefficients for u(z) given by (14)—torus with electric field
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Schmidt, A.G.M. Exact Solutions to Schrödinger Equation for a Charged Particle on a Torus in Uniform Electric and Magnetic Fields. Braz J Phys 50, 419–429 (2020). https://doi.org/10.1007/s13538-020-00764-9

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  • DOI: https://doi.org/10.1007/s13538-020-00764-9

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