dorsal/arxiv
View SchemaZeroth WKB Approximation in Quantum Mechanics
| Authors | M. N. Sergeenko |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0206179 |
| URL | https://arxiv.org/abs/quant-ph/0206179 |
Abstract
Solution of the Schr\"odinger's equation in the zero order WKB approximation is analyzed. We observe and investigate several remarkable features of the WKB$_0$ method. Solution in the whole region is built with the help of simple connection formulas we derive from basic requirements of continuity and finiteness for the wave function in quantum mechanics. We show that, for conservative quantum systems, not only total energy, but also momentum is the constant of motion. We derive the quantization conditions for two and more turning point problems. Exact energy eigenvalues for solvable and some ``insoluble'' potentials are obtained. The eigenfunctions have the form of a standing wave, $A_n\cos(k_nx+\delta_n)$, and are the asymptote of the exact solution.
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"abstract": "Solution of the Schr\\\"odinger\u0027s equation in the zero order WKB approximation\nis analyzed. We observe and investigate several remarkable features of the\nWKB$_0$ method. Solution in the whole region is built with the help of simple\nconnection formulas we derive from basic requirements of continuity and\nfiniteness for the wave function in quantum mechanics. We show that, for\nconservative quantum systems, not only total energy, but also momentum is the\nconstant of motion. We derive the quantization conditions for two and more\nturning point problems. Exact energy eigenvalues for solvable and some\n``insoluble\u0027\u0027 potentials are obtained. The eigenfunctions have the form of a\nstanding wave, $A_n\\cos(k_nx+\\delta_n)$, and are the asymptote of the exact\nsolution.",
"arxiv_id": "quant-ph/0206179",
"authors": [
"M. N. Sergeenko"
],
"categories": [
"quant-ph"
],
"title": "Zeroth WKB Approximation in Quantum Mechanics",
"url": "https://arxiv.org/abs/quant-ph/0206179"
},
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