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43 papers
Complex Periodic Potentials with a Finite Number of Band Gaps
Avinash Khare, Uday Sukhatme
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+…
Quasi-Periodic Solutions of Heun's Equation
Avinash Khare, Uday Sukhatme
By exploiting a recently developed connection between Heun's differential equation and the generalized associated Lamé equation, we not only recover the well known periodic solutio…
PT-Invariant Periodic Potentials with a Finite Number of Band Gaps
Avinash Khare, Uday Sukhatme
We obtain the band edge eigenstates and the mid-band states for the complex, PT-invariant generalized associated Lamé potentials $V^{PT}(x)=-a(a+1)m \sn^2(y,m)-b(b+1)m {\sn^2 (y+K(…
Cyclic Identities Involving Ratios of Jacobi Theta Functions
Avinash Khare, Arul Lakshminarayan, Uday Sukhatme
Identities involving cyclic sums of terms composed from Jacobi elliptic functions evaluated at equally shifted points were recently found. The purpose of this paper is to re-ex…
Periodic Potentials and Supersymmetry
Avinash Khare, Uday Sukhatme
We review the current status of one dimensional periodic potentials and also present several new results. It is shown that using the formalism of supersymmetric quantum mechanics,…
Analytically Solvable PT-Invariant Periodic Potentials
Avinash Khare, Uday Sukhatme
Associated Lamé potentials $V(x)=a(a+1)m\sn^2(x,m)+b(b+1)m{\cn^2 (x,m)}/{\dn^2(x,m)}$ are used to construct complex, PT-invariant, periodic potentials using the anti-isospectral tr…