# Coupled 2D harmonic oscillators

1. The problem statementView attachment 225935

## Homework Equations

3. I have rescaled coordinates which are X=(x1+x2)/√2 and Y=√3(x1-x2)/√2 for which the potential term becomes for a 2D harmonic oscillator of coordinates X and Y. But how to express Kinetic terms in terms of these new coordinates X and Y?

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Dr Transport
Gold Member
solve for $x_1$ and $x_2$ in terms of $X, Y$ then find the kinetic energy.

solve for $x_1$ and $x_2$ in terms of $X, Y$ then find the kinetic energy.
sorry sir I didn't get you here QM kinetic term is nedded

Dr Transport
$\hat{p}$ can be related to the $\dot{X}$, you just have to find the momentum operators in terms of your new coordinates.
$\hat{p}$ can be related to the $\dot{X}$, you just have to find the momentum operators in terms of your new coordinates.
$\hat{p}$ can be related to the $\dot{X}$, you just have to find the momentum operators in terms of your new coordinates.