dorsal/arxiv
View SchemaQuantum mechanics of the two-dimensional circular billiard plus baffle system and half-integral angular momentum
| Authors | R. W. Robinett |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0307035 |
| URL | https://arxiv.org/abs/quant-ph/0307035 |
| Journal | Eur. J. Phys. 24 (2003) 231 |
Abstract
We examine the quantum mechanical eigensolutions of the two-dimensional infinite well or quantum billiard system consisting of a circular boundary with an infinite barrier or baffle along a radius. Because of the change in boundary conditions, this system includes quantized angular momentum values corresponding to half-integral multiples of $\hbar/2$. We discuss the resulting energy eigenvalue spectrum and visualize some of the novel energy eigenstates found in this system. We also discuss the density of energy eigenvalues, $N(E)$, comparing this system to the standard circular well. These two billiard geometries have the same area (A=$\pi R^2$), but different perimeters ($P=2\pi R$ versus $(2\pi + 2) R$), and we compare both cases to fits of $N(E)$ which make use of purely geometric arguments involving only $A$ and $P$. We also point out connections between the angular solutions of this system and the familiar pedagogical example of the one-dimensional infinite well plus $\delta$-function potential.
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"abstract": "We examine the quantum mechanical eigensolutions of the two-dimensional\ninfinite well or quantum billiard system consisting of a circular boundary with\nan infinite barrier or baffle along a radius. Because of the change in boundary\nconditions, this system includes quantized angular momentum values\ncorresponding to half-integral multiples of $\\hbar/2$. We discuss the resulting\nenergy eigenvalue spectrum and visualize some of the novel energy eigenstates\nfound in this system. We also discuss the density of energy eigenvalues,\n$N(E)$, comparing this system to the standard circular well. These two billiard\ngeometries have the same area (A=$\\pi R^2$), but different perimeters ($P=2\\pi\nR$ versus $(2\\pi + 2) R$), and we compare both cases to fits of $N(E)$ which\nmake use of purely geometric arguments involving only $A$ and $P$. We also\npoint out connections between the angular solutions of this system and the\nfamiliar pedagogical example of the one-dimensional infinite well plus\n$\\delta$-function potential.",
"arxiv_id": "quant-ph/0307035",
"authors": [
"R. W. Robinett"
],
"categories": [
"quant-ph"
],
"journal_ref": "Eur. J. Phys. 24 (2003) 231",
"title": "Quantum mechanics of the two-dimensional circular billiard plus baffle system and half-integral angular momentum",
"url": "https://arxiv.org/abs/quant-ph/0307035"
},
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