dorsal/arxiv
View SchemaZero-curvature solutions of the one-dimensional Schrodinger equation
| Authors | M. Belloni, M. A. Doncheski, R. W. Robinett |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0410104 |
| URL | https://arxiv.org/abs/quant-ph/0410104 |
Abstract
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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"date_created": "2026-03-02T18:02:10.390000Z",
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"abstract": "We discuss special k=sqrt{2m(E-V(x))/\\hbar^2}=0 (i. e. zero-curvature)\nsolutions of the one-dimensional Schrodinger equation in several model systems\nwhich have been used as idealized versions of various quantum well structures.\nWe consider infinite well plus Dirac delta function cases (where E=V(x)=0) and\npiecewise-constant potentials, such as asymmetric infinite wells (where\nE=V(x)=V_0\u003e0). We also construct supersymmetric partner potentials for several\nof the zero-energy solutions in these cases. One application of zero-curvature\nsolutions in the infinite well plus delta-function case is the construction of\n`designer\u0027 wavefunctions, namely zero-energy wavefunctions of essentially\narbitrary shape, obtained through the proper placement and choice of strength\nof the delta-functions.",
"arxiv_id": "quant-ph/0410104",
"authors": [
"M. Belloni",
"M. A. Doncheski",
"R. W. Robinett"
],
"categories": [
"quant-ph"
],
"title": "Zero-curvature solutions of the one-dimensional Schrodinger equation",
"url": "https://arxiv.org/abs/quant-ph/0410104"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "41efbcaa-dd93-434a-b358-a7838735fad6",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
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