Solving the Schrödinger equation of an electron in a periodic crystal potential through elliptic functions

DOI10.1007/s10910-021-01269-9zbMath1476.81039arXiv2108.07156OpenAlexW3179610043MaRDI QIDQ2230700

Luca Nanni

Publication date: 28 September 2021

Published in: Journal of Mathematical Chemistry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2108.07156

zbMATH Keywords

Schrödinger equationelliptic functionsperiodic potentialelectronic band structure

Mathematics Subject Classification ID

Statistical mechanics of crystals (82D25) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Elliptic functions and integrals (33E05) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35)

Cites Work

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• Exactly solvable associated Lamé potentials and supersymmetric transformations
• Application of elliptic Riemannian geometry to problems of crystallography
• A METHOD TO CONSTRUCT WEIERSTRASS ELLIPTIC FUNCTION SOLUTION FOR NONLINEAR EQUATIONS
• Gauss
• Calculation of the Taylor Series Expansion Coefficients of the Jacobian Elliptic Function sn(x, k)
• Generalized Lamé functions. I. The elliptic case
• Computation of elliptic functions
• The Classification of Non-Euclidean Plane Crystallographic Groups
• Wave Functions in a Periodic Potential