## Abstract

We discuss special k = √2m(E - V(x))/ℏ^{2} = 0 (i.e. zero-curvature) solutions of the one-dimensional Schrödinger 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 δ-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 δ-functions.

Original language | English (US) |
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Pages (from-to) | 122-126 |

Number of pages | 5 |

Journal | Physica Scripta |

Volume | 72 |

Issue number | 2-3 |

DOIs | |

State | Published - 2005 |

## All Science Journal Classification (ASJC) codes

- Atomic and Molecular Physics, and Optics
- Mathematical Physics
- Condensed Matter Physics