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math-ph2011★ 26 cited
Transmutations for Darboux transformed operators with applications
Vladislav V. Kravchenko, Sergii M. Torba
We solve the following problem. Given a continuous complex-valued potential q_1 defined on a segment [-a,a] and let q_2 be the potential of a Darboux transformed Schrödinger operat…
math.CA2011★ 49 cited
Transmutations, L-bases and complete families of solutions of the stationary Schrödinger equation in the plane
Hugo M. Campos, Vladislav V. Kravchenko, Sergii M. Torba
An L-basis associated to a linear second-order ordinary differential operator L is an infinite sequence of functions {ϕ_k}_{k=0}^{\infty} such that Lϕ_k=0 for k=0,1, Lϕ_k=k(k-1)ϕ_{…