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I have some questions about treatment of Schrodinger equation where ## \hat{V}(\theta)##, the potential energy part of Hamiltonian ##\hat{H}=\hat{T}(\theta)+\hat{V}(\theta)## is a trigonometric function like:

##\hat{V}(\theta) = a sin(\theta)##

or

##\hat{V}(\theta) = a cos(\theta)+ b sin(c\theta)## where ##\theta## is an angular variable.

I read something in solid-state physics that a system which evolve inside a periodical potential ends up with energy bands as eigenvalues solutions.

Do I have the same case here, with those two examples of potential energy?

In other words, will I obtain energy band too, even here I have nothing to do with lattice nor crystals?

Thank you everybody.

Konte

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# I Periodic potential - energy bands

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