New Soluble Energy Band Problem

Publisher Website

15 November 1958

journal article
research article
Published by American Physical Society (APS) in Physical Review B

Vol. 112 (4) , 1137-1140
https://doi.org/10.1103/physrev.112.1137

Abstract

The Schrödinger equation for

V (x) = - V_{0} {csc}^{2} (\frac{π x}{a})

is solved.

E (k)

and the effective mass are examined along with the wave functions for various values of the parameter (

V_{0} a^{2}

). It is found that the wave functions have intermediate forms even when

m^{*} ≅ m

,

m^{*} ≅ \infty

, and that the weak- and tight-binding approximations are not valid in these regions.

Keywords

This publication has 7 references indexed in Scilit:

Discrete States for Singular Potential Problems
Physical Review B, 1958
A Soluble Problem in Energy Bands
Physical Review B, 1952
Singular Potentials
Physical Review B, 1950
Energy Bands and Wave Functions in Periodic Potentials
Physical Review B, 1949
On the Constitution of Metallic Sodium
Physical Review B, 1933
Quantum mechanics of electrons in crystal lattices
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