# Spectra of one dimensional Schrodinger operators [on hold]

I am trying to understand how to compute the spectra of one-dimensional Schrödinger operators $$\mathcal{L}:=-\partial_x^2+V,$$ where $$V$$ is a bounded function in the whole line. I am particularly interested in understanding the discrete spectra for the case $$V:=1-2\,\text{sech}^2(x)$$, which is a "localized" function but it has no sign neither decay. I think this case shouldn't be difficult, but I do not know how to compute it.

Is there any good reference where I can learn how to do it? Or can someone give me some hints? I would really appreciate it.

## put on hold as off-topic by Carlo Beenakker, Alexandre Eremenko, András Bátkai, LSpice, arsmathJul 16 at 13:59

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