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hmdkdl
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Homework Statement
Hi,
I want to diagonalize the Hamiltonian:
Homework Equations
[itex] H=\phi a^{\dagger}b + \phi^{*} b^{\dagger}a [/itex]
a and b are fermionic annihilation operators and [itex]\phi[/itex] is some complex number.
The Attempt at a Solution
Should I use bogoliubov tranformations? I have put the following:
[itex] a = u c + v d^{\dagger} [/itex]
[itex] b = w c + z d^{\dagger} [/itex]
(which c and d are some other fermionic annihilation operators and u, v, w, z complex numbers) into hamiltonian but I cannot find the final answer (it does not seem straightforward).. Is it correct? and if so how can I find the final answer.
Thanks in advance,