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Question: a particle is in a 2dimension potential vxy 12...

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A particle is in a 2-dimension potential V(x,y) = 1/2 uw^2(x^2+y^2 +2lambdaxy) where w is the mass of the particle and lambda < 1. What are energy levels for the stationary solutions? Note: This only asks about the energy.

Hint: you will have to do a change of variables so that the potential will look like the sum of two harmonic oscillators with the new variables.

Further Hint: The new pair of variables can be a= 1/sqrt(2)(x+y), b=1/sqrt(2) (x-y).

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