A nonselfadjoint problem
I a have a problem:
U''(x) - lambda^2 * U(x)=0 0<= x <= 1
BC:
U'(0) = lambda * U(0)
U'(1) = - lambda * U(1)
where lambda is an eigenvalue.
Once solved lambda and its eigenfunctions are complex. Orthogonality
conditions involve eigenvalues and boundary terms.
Now, I'd like to represent a nice function with these eigenfunctions.
The problem is that these eigenfunctions are not orthogonal, so I
don't know how to calculate coeficients of the series in closed form.
I am not able to find anything on this kind of eigenvalue problem
which acctually arises from a physical model in vibrations.
Any ideas?
.
Relevant Pages
- Re: Orthogonal Eigenfunctions
... > eigenfunctions of an orthonormal set are at right angles to one ... > another in multidimensional eigenvalue space ... ... > can tell us the probability of being in a particular state but not of ... I have a vague glimmer of a recollection that the orthogonality ...
(sci.physics) - Re: ? Measuring eigenvalues
... > and eigenfunctions. ... PDEs and ODEs are the basis of almost all modern physics. ... molecules, molecular vibrations, and mechanical vibrations in strings, ... every line in a spectrum is an eigenvalue. ...
(sci.physics) - Re: ? Measuring eigenvalues
... >remember is that the eigenfunctions depend on the boundary conditions. ... >e.g. the time component will be expand the space component will ... >the eigenvalue would measure the decay rate of any disturbances in ...
(sci.physics) - Re: Orthogonal Eigenfunctions
... > Can anyone give me a physical interpretation of what orthogonal ... > eigenfunctions of an orthonormal set are at right angles to one ... The various energy eigenfunctions (for a given physical ... orthogonality means that in state E1 the probability of finding the ...
(sci.physics) - Re: Eigenvectors, Eigenfunctions,...
... understand the basics of how to solve them but I am left with a number of ... What exactly does an eigenvalue, -vector, -function represent? ... F=ma is a familiar expression of Newton's law on how a particle moves. ... The eigenvectors (or eigenfunctions, same thing) are related ...
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