Let $B$ be a magnetic field, let $\mathbf{a}$ be a vector and let $\Psi$ be the wave function. If $\mathcal{H}(B) = (-i\nabla + B\mathbf{a})^2$, where $\nabla$ is the gradient, then the time-independent magnetic Schrodinger equation is given by

$$\mathcal{H}(B) \Psi = \lambda \Psi$$

What is a simple way of finding the eigenvalue and eigenfunction solution to the above equation?

  • 1
    $\begingroup$ It is a very delicate issue. You can find many papers by Bernhard Helffer on the internet. Here is another source: mat.puc.cl/~graikov/noop.pdf $\endgroup$
    – Siminore
    Commented Mar 21, 2014 at 8:51
  • $\begingroup$ Are B and a constant or do they depend on coordinates? $\endgroup$
    – Urgje
    Commented Mar 21, 2014 at 9:50


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