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Hi all.

I have a Hamiltonian given by:

[tex]

H = H_x + H_y = -\frac{\hbar^2}{2m}(d^2/dx^2 + d^2/dy^2).

[/tex]

Now I have a stationary state on the form [itex]\psi(x,y)=f(x)g(y)[/itex]. According to my teacher, then the Hamiltonian can be split up, i.e. we have the two equations:

[tex]

H_x f(x) = E_xf(x) \qquad \text{and}\qquad H_y g(y)=E_yg(y).

[/tex]

I can't see why this must be true. Inserting in the time-independent SchrÃ¶dinger-equation doesn't give me these expressions. What am I missing here?

Thanks in advance.

Best regards,

Niles

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# QM: Splitting up the Hamiltonian

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