Urkel
May23-11, 06:05 PM
Hello everyone,
I am solving an eigenvalue problem. Right now, I would like to know;
How to determine the degeneracy of eigensolution of sturm-liouville differential eigenvalue problem?
I have an eigenvalue sturm-liouville problem H f(y) = E f(y) where H is a differential operator and E is the eigenvalue that can be re-written as the following high order PDE
[(E + a ∂_y^2 - b y) (E - a ∂_y^2- b y) + k^2 ]f(y)=0
a, b are constants. ∂_y^2 is 2nd derivative w.r.t. y
How to determine if the eigenvalue is degenerate with respect to k, that is, it does not depend on k? k is constant.
That is, can we find several eigenfunctions that correspond to the same eigenvalue E?
How to prove that the eigenvalue is degenerate or not? Any theorem on that?
I hope someone who is expert in theory of PDE can help me on this.
Thanks
I am solving an eigenvalue problem. Right now, I would like to know;
How to determine the degeneracy of eigensolution of sturm-liouville differential eigenvalue problem?
I have an eigenvalue sturm-liouville problem H f(y) = E f(y) where H is a differential operator and E is the eigenvalue that can be re-written as the following high order PDE
[(E + a ∂_y^2 - b y) (E - a ∂_y^2- b y) + k^2 ]f(y)=0
a, b are constants. ∂_y^2 is 2nd derivative w.r.t. y
How to determine if the eigenvalue is degenerate with respect to k, that is, it does not depend on k? k is constant.
That is, can we find several eigenfunctions that correspond to the same eigenvalue E?
How to prove that the eigenvalue is degenerate or not? Any theorem on that?
I hope someone who is expert in theory of PDE can help me on this.
Thanks