0
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1answer
18 views

When finding the frequencies of normal modes, can you have a negative frequency?

Do you simply just consider the positive solutions? I tried a google search but didn't find anything quickly. The work I am studying is Lagrangian systems.
2
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0answers
88 views

Solving Generalized Eigenvalue Problem perturbatively

Let me formulate the problem to convey my notation. I have a matrix $A$ which is hermitian - and is diagonalisable by a transformation $$ U_A A\,\,U_A^{-1} = A_{diag}$$ Now the matrix is changed, ...
1
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1answer
91 views

Difference in sound between a string and a pipe

I am told that I can model the vibration of a guitar string of length $l >0$ by the following Sturm-Liouville equation $$ -u'' = \lambda u \: \: \text{ on } [0,l],$$ with boundary conditions ...
1
vote
1answer
113 views

Eigenstate and quantum mechanics position opperator

Quantum mechanics math question: Suppose that there is eigenstate $|q \rangle$ where $q$ is position observable . The question is, 1) What is eigenstate? How is this different from eigenvector? ...
5
votes
1answer
258 views

Physical interpretation: weighted eigenvalues of the Laplacian with a potential

I've already posted this question on Physics.SE, but I thougth it could be useful to ask also here. No problem if moderators will ask me to cancel this thread... But, please, have mercy! :-D Let ...
1
vote
1answer
132 views

Coupled Torsion Pendulum Eigenvectors

I was trying to solve a coupled torsion pendulum (note this is for an assignment, so please just guidance, no solutions), consisting of two rods suspended on a vertical wire clamped at either end. ...