Zero-curvature solutions of the one-dimensional Schrodinger equation

Details Zero-curvature solutions of the one-dimensional Schrodinger equation Zero-curvature solutions of the one-dimensional Schrodinger equation

2004-10-13

arxiv.org/abs/quant-ph/0410104v1

Physics

Quantum Physics

13 pages, 2 embedded .eps figures; a slightly shortened version of this manuscript was submitted to Phys. Rev. A as a Brief Re

Scientific paper

We discuss special k=sqrt{2m(E-V(x))/\hbar^2}=0 (i. e. zero-curvature) solutions of the one-dimensional Schrodinger equation in several model systems which have been used as idealized versions of various quantum well structures. We consider infinite well plus Dirac delta function cases (where E=V(x)=0) and piecewise-constant potentials, such as asymmetric infinite wells (where E=V(x)=V_0>0). We also construct supersymmetric partner potentials for several of the zero-energy solutions in these cases. One application of zero-curvature solutions in the infinite well plus delta-function case is the construction of `designer' wavefunctions, namely zero-energy wavefunctions of essentially arbitrary shape, obtained through the proper placement and choice of strength of the delta-functions.

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