论文标题
不对称的谐波振荡器
Asymmetric harmonic oscillator
论文作者
论文摘要
提出了一维非对称量子谐波振荡器的溶液。例如，可以通过使用两个弹簧来实现不对称性，将一个弹簧与质量粘合在一起，第二弹簧与平衡点中的质量自由连接，并且位于第一个弹簧内或外部，仅在质量上仅来自右侧的接触点。我们研究了量子谐波振荡器的光谱，该量子振荡器在平衡位置的左侧具有弹簧常数$ k _- $，在平衡位置的右侧具有弹簧常数$ k_ +$。在提出的情况下，第二个字符串的接触点是第一个字符串的平衡点。讨论了本征函数的明确形式，即计算特征值和本征函数的特性的方法。
The solution of one--dimensional asymmetric quantum harmonic oscillator is presented. The asymmetry can be realized, for example, by using two springs, one spring is glued with the mass, and the second spring is freely connected with the mass in the equilibrium point and it is located inside or outside the first spring which acts on the mass only from the contact point on the right. We study the spectrum of a quantum harmonic oscillator, which has a spring constant $ k_-$ to the left of the equilibrium position and a spring constant $ k_ +$ to the right of the equilibrium position. In the presented case the contact point of the second string is the equilibrium point of the first string. The explicit form of eigenfunctions, the way to calculate the eigenvalues and the properties of the eigenfunctions are discussed.
