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**1. The problem statement, all variables and given known data**

Hi all.

Lets I have a system, whose Hamiltonian is given by [itex]H = p_1 + p_2[/itex], where p

_{i}is the momentum of

*i*, where this

*i*can be whatever, e.g. momentum in some particular direction. When the Hamiltonian is given on this form, do I know for certain that the eigenenergies of the system are on the form:

[tex]

E_{m,n} = f(m) + g(n),

[/tex]

where

*f*and

*g*are two functions that depend on respectively m and n? I.e. I am wondering if the eigenenergies of the system follow the same form as the Hamiltonian.

I hope you can help.

Best regards,

Niles.