How to Determine the Eigenenergy of This Hamiltonian?

[john go]

The Hamiltonian is given:

H=Aâ†â + B(â + â†)

where â is annihilation operator and ↠is creation operator,
and A and B are constants.

How can I get the eigenenergy of this Hamiltonian?

The given hint is "Use new operator b = câ + d, b† =c↠+ d
(c and d are constants, too)

But I can't use that hint properly.

 

[Meir Achuz]

Form H=b*b. Compare this with the original H, and solve for c and d in terms
of A and B.