Physics – Quantum Physics
Scientific paper
2006-02-13
Physics
Quantum Physics
33 pages, 0 figures
Scientific paper
10.1063/1.2204810
We obtain several new results for the complex generalized associated Lame potential V(x)= a(a+1)m sn^2(y,m)+ b(b+1)m sn^2(y+K(m),m) + f(f+1)m sn^2(y+K(m)+iK'(m),m)+ g(g+1)m sn^2(y+iK'(m),m), where y = x-K(m)/2-iK'(m)/2, sn(y,m) is a Jacobi elliptic function with modulus parameter m, and there are four real parameters a,b,f,g. First, we derive two new duality relations which, when coupled with a previously obtained duality relation, permit us to relate the band edge eigenstates of the 24 potentials obtained by permutations of the four parameters a,b,f,g. Second, we pose and answer the question: how many independent potentials are there with a finite number "a" of band gaps when a,b,f,g are integers? For these potentials, we clarify the nature of the band edge eigenfunctions. We also obtain several analytic results when at least one of the four parameters is a half-integer. As a by-product, we also obtain new solutions of Heun's differential equation.
Khare Avinash
Sukhatme Uday
No associations
LandOfFree
Complex Periodic Potentials with a Finite Number of Band Gaps does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Complex Periodic Potentials with a Finite Number of Band Gaps, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Complex Periodic Potentials with a Finite Number of Band Gaps will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-167552