[coupled harmonic oscillators] old thread- need elaboration

[rsaad]

Hi
Can someone please explain the answer to the following thread? I tried uncoupling the Hamiltonian but to no avail.

https://www.physicsforums.com/showthread.php?t=602106

Thank you.

 

[mfb]

Did you try the proposed rotation?

$x'=\cos(\alpha)x + \sin(\alpha)y$, $y'=-\sin(\alpha)x + \cos(\alpha)y$

Where α has to be determined to uncouple the Hamiltonian.

 

[rsaad]

Yes i tried but I am still getting xy term

 

[mfb]

You could show your work here, this would help to find the error.