Is this complex? Everything I've checked (here and here) appears to be real.jedishrfu said:Would the square well be such a problem?
Sorry, perhaps I did not specify: I mean't so that the eigenvalues/vectors have a real and complex part. Perhaps something like ##x''+ix'+x=0##, but I'm at a loss.Haborix said:I take you to mean the function is complex valued over the real line, so it could be written ##f=g(x)+ih(x)##.
Does not need to be a real-world example. I am looking for a good toy problem to work with.Haborix said:Edit: I also meant to ask if you are looking for a real-world example.
A simple, linear, complex, eigenvalue BVP (boundary value problem) is a type of mathematical problem that involves finding the values of a function at multiple points, subject to certain boundary conditions. The function is typically a linear combination of simpler functions, and the problem involves finding the eigenvalues (or characteristic values) that satisfy the given conditions.
In a simple eigenvalue BVP, the eigenvalues are distinct and the corresponding eigenvectors are linearly independent. In a complex eigenvalue BVP, the eigenvalues may be repeated or complex, and the corresponding eigenvectors may not be linearly independent. This can make the problem more challenging to solve.
In a linear eigenvalue BVP, the function and its derivatives appear in a linear form. This means that the coefficients of the function and its derivatives are constant. In a nonlinear eigenvalue BVP, the function and its derivatives appear in a nonlinear form, meaning the coefficients may vary with the function itself.
Eigenvalue BVPs are used in many scientific fields, including physics, engineering, and mathematics. They are particularly useful in studying systems that exhibit oscillatory behavior, such as vibrating structures or quantum mechanical systems. They also have applications in solving differential equations and analyzing the stability of systems.
There are several methods for solving eigenvalue BVPs, including analytical methods such as separation of variables and numerical methods such as finite difference or finite element methods. The specific method used depends on the complexity of the problem and the desired level of accuracy. In some cases, the eigenvalues and eigenvectors can also be approximated using computer algorithms.