Coupled 2D harmonic oscillators

  • #1
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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Answers and Replies

  • #2
Dr Transport
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solve for [itex] x_1 [/itex] and [itex]x_2 [/itex] in terms of [itex] X, Y[/itex] then find the kinetic energy.
 
  • #3
solve for [itex] x_1 [/itex] and [itex]x_2 [/itex] in terms of [itex] X, Y[/itex] then find the kinetic energy.
sorry sir I didn't get you here QM kinetic term is nedded
 
  • #4
Dr Transport
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[itex] \hat{p} [/itex] can be related to the [itex] \dot{X} [/itex], you just have to find the momentum operators in terms of your new coordinates.
 
  • #5
[itex] \hat{p} [/itex] can be related to the [itex] \dot{X} [/itex], you just have to find the momentum operators in terms of your new coordinates.
sir but in calculating p2 there will be again interaction term between X And Y
Sir I am actually trying to find d2/dx12 in terms of d2/dX2 and d2/dY2
 
  • #6
[itex] \hat{p} [/itex] can be related to the [itex] \dot{X} [/itex], you just have to find the momentum operators in terms of your new coordinates.
O thank you sir I have got it
The ans is option B
 

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