ELECTRON EIGENSTATES IN UNIFORM MAGNETIC FIELDS

The purpose of this paper is to show in detail how the electron energy-eigenvalue spectrum changes from the form [formula omitted] in a finite magnetic field to the free-particle form [formula omitted] in zero magnetic field. We consider an electron confined to a “box” of finite volume and calculate the exact eigenstates for arbitrary magnetic field strengths. When the electron cyclotron radius [formula omitted] is small compared to the dimensions of the box, we get the spectrum [formula omitted], and when it is large we get [formula omitted]. The key to this demonstration is a mathematical identity which relates the magnetic eigenfunctions to the free-particle eigenfunctions. Magnetic corrections to the spectrums [formula omitted] are obtained without the use of quantum mechanical perturbation theory. © 1969, American Association of Physics Teachers. All rights reserved.