二维圆形台球加挡板系统的量子力学和半积分angular momentum
Quantum mechanics of the two-dimensional circular billiard plus baffle system and half-integral angular momentum
摘要：
研究了二维无限深阱或量子台球系统的量子力学本征解，该系统由一个沿半径方向带有无限大势垒或挡板的圆形边界组成。由于边界条件的变化，该系统包括对应于$\hbar/2$的半整数倍的量化角动量值。我们讨论了由此产生的能量本征值谱和可视化的一些新的能量本征态在这个系统中发现。我们还讨论了能量本征值的密度，$N(E)$，比较这个系统的标准圆形井。这两个台球几何形状有相同的面积（A= $πR^2$），但不同的周长（$P=2πR$与$(2π+ 2) R$），我们比较这两种情况下适合的$N(E)$利用纯粹的几何参数只涉及$A$和$P$。我们还指出了这个系统的角的解决方案和熟悉的教学的例子，一维无限好加上$δ$ -功能潜力之间的连接。
英文摘要：
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=$πR^2$), 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.
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