论文标题
离散量子谐波振荡器和Kravchuk变换
Discrete quantum harmonic oscillator and Kravchuk transform
论文作者
论文摘要
我们考虑对谐波振荡器的特殊离散化，该谐波振荡器从数值的角度接受了具有吸引力的特性的特征函数的正交基础。我们在分析上证明了这些离散函数几乎二阶收敛到Hermite函数，对于大量模式而言，它们均匀地证明了这些函数。然后，我们描述了模拟这些本征函数和相应转换的有效方法。我们最终显示了一些数值实验，以证实我们的不同结果。
We consider a particular discretization of the harmonic oscillator which admits an orthogonal basis of eigenfunctions called Kravchuk functions possessing appealing properties from the numerical point of view. We analytically prove the almost second-order convergence of these discrete functions towards Hermite functions, uniformly for large numbers of modes. We then describe an efficient way to simulate these eigenfunctions and the corresponding transformation. We finally show some numerical experiments corroborating our different results.
