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This paper considers a generalised Strum-Liouville equation, that is equations of the form

$$ \left[-\frac{d}{dx}p(x)\frac{d}{dx}-\frac{i}{2}\left(\lambda_1(x)\frac{d}{dx}+\frac{d}{dx}\lambda_2(x)\right)+v(x)\right]\psi(x)=\left(\frac{\omega}{c}\right)^2\psi(x)\tag{1} $$

and calls $\lambda_i(x)\in\mathbb{C}$ complex gauge potentials. What do these potentials represent physically?

In particular I'm interested in the case where $p(x)$ is constant and $v(x)=0$ so that $\psi(x)$ represents some kind of time harmonic wave equation.

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    $\begingroup$ Do you understand what a "gauge potential" is in the Hermitian case where $\lambda\in {\mathbb R}$? $\endgroup$
    – mike stone
    Commented Jan 30 at 12:25
  • $\begingroup$ No, not really.. $\endgroup$
    – bas
    Commented Jan 30 at 12:29
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    $\begingroup$ It would be a good idea then to read up on the Schroedinger equation in a magnetic field. In the one dimensional case in your paper you can probably absorb the $\lambda$ into the $\psi$ field by means of a gauge transformation. Again you will need to read a book on quantum mechanics to see how this works. $\endgroup$
    – mike stone
    Commented Jan 30 at 12:32

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