### 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 ℏ/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 = πR^{2}), but different perimeters (P = 2πR versus (2π + 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 δ-function potential.

Original language | English (US) |
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Pages (from-to) | 231-243 |

Number of pages | 13 |

Journal | European Journal of Physics |

Volume | 24 |

Issue number | 3 |

DOIs | |

State | Published - May 1 2003 |

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### All Science Journal Classification (ASJC) codes

- Physics and Astronomy(all)

### Cite this

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**Quantum mechanics of the two-dimensional circular billiard plus baffle system and half-integral angular momentum.** / Robinett, Richard Wallace.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Quantum mechanics of the two-dimensional circular billiard plus baffle system and half-integral angular momentum

AU - Robinett, Richard Wallace

PY - 2003/5/1

Y1 - 2003/5/1

N2 - 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 ℏ/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 = πR2), but different perimeters (P = 2πR versus (2π + 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 δ-function potential.

AB - 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 ℏ/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 = πR2), but different perimeters (P = 2πR versus (2π + 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 δ-function potential.

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U2 - 10.1088/0143-0807/24/3/302

DO - 10.1088/0143-0807/24/3/302

M3 - Article

AN - SCOPUS:0037850044

VL - 24

SP - 231

EP - 243

JO - European Journal of Physics

JF - European Journal of Physics

SN - 0143-0807

IS - 3

ER -