Energy spectrum from a hamiltonian

[Fixxxer125]

Hi there, just wondered if anyone could help me...
If I am given a hamiltonian describing a particle in one dimension

H=p^2/2m +1/2 (γ(x-a)^1/2) + K(x-b) how do I go about finding the eigenstates and eigenvalues of this hamiltonian?
Many thanks

 

[dextercioby]

For that classical Hamiltonian, can you think of a canonical transformation in phase space to get rid of the square root ?