Quoting Eugene Salamin <gene_salamin@yahoo.com>:
Now for my question. Suppose I'm only interested in the energy bands, and I don't care about the actual wave function u(x). Then, given some value of E, is there a way to calculate tr(M(E)) without having to solve the differential equation?
As far as I know, which may not be all that much, there is no shortcut. However, depending on your potential, you may be able to develop a good approximation and relate your answer to the stability chart of the Mathieu functions. That would work if your potential were close to a cosine and splitting the coefficient matrix would give a new equation for the coefficients of the desired solution in terms of Mathieu functions. But if the new coefficient were small, a couple of terms of the power series for the new solution might suffice. I've done this for other equations, but never tried it in the Mathieu environment. - hvm ------------------------------------------------- www.correo.unam.mx UNAMonos Comunicándonos