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?
 

Attachments

Last edited:

Answers and Replies

  • #2
Dr Transport
Science Advisor
Gold Member
2,457
593
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
Science Advisor
Gold Member
2,457
593
[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
 

Related Threads on Coupled 2D harmonic oscillators

  • Last Post
Replies
8
Views
9K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
1
Views
3K
  • Last Post
Replies
0
Views
2K
  • Last Post
Replies
1
Views
5K
  • Last Post
Replies
24
Views
5K
  • Last Post
Replies
2
Views
5K
  • Last Post
Replies
1
Views
3K
Replies
8
Views
2K
Replies
1
Views
1K
Top