dorsal/arxiv
View SchemaA Nonperturbative Perspective on Inner Product Quantization: Highly Accurate Solutions to the Schr{\"o}dinger Equation
| Authors | C. J. Tymczak, G. S. Japaridze, C. R. Handy, Xiao-Qian Wang |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9707005 |
| URL | https://arxiv.org/abs/quant-ph/9707005 |
Abstract
We devise a new and highly accurate quantization procedure for the inner product representation, both in configuration and momentum space. Utilizing the representation $\Psi(\xi) = \sum_{i}a_i[E]\xi^i R_{\beta}(\xi)$, for an appropriate reference function, $R_{\beta}(\xi)$, we demonstrate that the (convergent) zeroes of the coefficient functions, $a_i[E] = 0$, approximate the exact bound/resonance state energies with increasing accuracy as $i \to \infty$. The validity of the approach is shown to be based on an extension of the Hill determinant quantization procedure. Our method has been applied, with remarkable success, to various quantum mechanical problems.
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"date_created": "2026-03-02T18:02:41.347000Z",
"date_modified": "2026-03-02T18:02:41.347000Z",
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"abstract": "We devise a new and highly accurate quantization procedure for the inner\nproduct representation, both in configuration and momentum space. Utilizing the\nrepresentation $\\Psi(\\xi) = \\sum_{i}a_i[E]\\xi^i R_{\\beta}(\\xi)$, for an\nappropriate reference function, $R_{\\beta}(\\xi)$, we demonstrate that the\n(convergent) zeroes of the coefficient functions, $a_i[E] = 0$, approximate the\nexact bound/resonance state energies with increasing accuracy as $i \\to\n\\infty$. The validity of the approach is shown to be based on an extension of\nthe Hill determinant quantization procedure. Our method has been applied, with\nremarkable success, to various quantum mechanical problems.",
"arxiv_id": "quant-ph/9707005",
"authors": [
"C. J. Tymczak",
"G. S. Japaridze",
"C. R. Handy",
"Xiao-Qian Wang"
],
"categories": [
"quant-ph"
],
"title": "A Nonperturbative Perspective on Inner Product Quantization: Highly Accurate Solutions to the Schr{\\\"o}dinger Equation",
"url": "https://arxiv.org/abs/quant-ph/9707005"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "e3ad236f-bf5f-42b3-b80a-1e78491256cb",
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"variant": "snapshot-2026-03-01",
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