- #1

holden

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Having a lot of trouble with this one. I'm given that the Hamiltonian of a certain particle can be expressed by H = A(a+a) + B(aa+), where A and B are constants and a+ and a are the raising and lowering operators, respectively. I'm supposed to find the energies of the stationary states for the particle.

I'm also given that the operators satisfy the communtation relation [a, a+] = 1. So from this I'm getting [tex]aa_+\psi - a_+a\psi = \psi[/tex]. From the Hamiltonian I have [tex]A(a_+a)\psi + B(aa_+)\psi = E\psi[/tex]. I tried using the first equation to replace one of the terms on the left side in the second, to get [tex]A(aa_+\psi - \psi) + B(aa_+\psi) = E\psi[/tex]... but I don't see how this really helps. I'm stuck on what to do next, so any help would be appreciated :)

I'm also given that the operators satisfy the communtation relation [a, a+] = 1. So from this I'm getting [tex]aa_+\psi - a_+a\psi = \psi[/tex]. From the Hamiltonian I have [tex]A(a_+a)\psi + B(aa_+)\psi = E\psi[/tex]. I tried using the first equation to replace one of the terms on the left side in the second, to get [tex]A(aa_+\psi - \psi) + B(aa_+\psi) = E\psi[/tex]... but I don't see how this really helps. I'm stuck on what to do next, so any help would be appreciated :)

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