- #1

- 24

- 0

*standard*way of finding out the spectrum of a Hamiltionian given a specific [tex]H[/tex]. For example, [tex]H = -\Delta - 10|x|^{3} + |x|^{4}[/tex] or [tex]H = -\Delta -(1+|x|)^{-2}[/tex].

I don't need answers to the above, I just want to know if one can describe the spectrums of Hamiltinian's such as those, in an easy fashion. I'm looking at examples from the textbook and something as simple as the operator [tex]x[/tex] or even momentum [tex]p[/tex] have a fairly complicated derivation to show their spectrum is [tex][0,\infty)[/tex].

Does the variation principle come into play at all? Can anyone find examples on the web, like a ton of them, so that I can learn and get the hang of it? Thanks!