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## Homework Statement

A two-dimensional harmonic oscillator is described by a potential of the form

V(x,y) = 1/2 m [tex] \omega^{2}[/tex](x[tex]^{2}[/tex]+y[tex]^{2}[/tex] + [tex]\alpha (x-y)^{2}[/tex]

where [tex]\alpha[/tex] is a positive constant.

## Homework Equations

Find the ground-state energy of the oscillator

## The Attempt at a Solution

I have tried to plug in the energy of SHO for each dimension x,y; yielding E = h_bar [tex]\omega[/tex](n

_{x}+1/2) + h_bar [tex]\omega[/tex](n

_{y}+1/2)

which method should I use to solve the third term i.e. [tex]\alpha (x-y)^{2}[/tex]?