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## Main Question or Discussion Point

Hi everyone!

I am answering this problem which is about the eigenvalues and eigenfunctions of the Hamiltonian given as:

H = 5/3(a+a) + 2/3(a^2 + a+^2), where a and a+ are the ladder operators.

It was given that a = (x + ip)/√2 and a+ = (x - ip)/√2. Furthermore, x and p satisfies the commutation relation [x,p] = i, i.e., p = -i (d/dx).

The question is find the energy eigenvalues and ground state eigenfunction. Is this problem related to the quantum harmonic oscillator? I can't solve it using the usual Hψ = Eψ approach.

Thanks a lot!

I am answering this problem which is about the eigenvalues and eigenfunctions of the Hamiltonian given as:

H = 5/3(a+a) + 2/3(a^2 + a+^2), where a and a+ are the ladder operators.

It was given that a = (x + ip)/√2 and a+ = (x - ip)/√2. Furthermore, x and p satisfies the commutation relation [x,p] = i, i.e., p = -i (d/dx).

The question is find the energy eigenvalues and ground state eigenfunction. Is this problem related to the quantum harmonic oscillator? I can't solve it using the usual Hψ = Eψ approach.

Thanks a lot!