论文标题
小波的量子力学
Quantum Mechanics in Wavelet Basis
论文作者
论文摘要
我们描述了一种多尺度的分辨率方法，用于使用Daubechies小波在量子力学中分析问题。在此基础上，量子系统波函数的扩展允许将每个基函数自然解释为特定位置特定分辨率的量子波动。在此基础上构建的Hamiltonian矩阵描述了不同长度尺度之间的耦合，因此可以进行直观的体积和分辨率截断。在具有自然长度尺度的量子机械问题中，可以通过简单的矩阵对角线化获得问题的近似解决方案。我们使用标准量子机械简单谐波振荡器的示例来说明这种方法。
We describe a multi-scale resolution approach to analyzing problems in Quantum Mechanics using Daubechies wavelet basis. The expansion of the wavefunction of the quantum system in this basis allows a natural interpretation of each basis function as a quantum fluctuation of a specific resolution at a particular location. The Hamiltonian matrix constructed in this basis describes couplings between different length scales and thus allows for intuitive volume and resolution truncation. In quantum mechanical problems with a natural length scale, one can get approximate solution of the problem through simple matrix diagonalization. We illustrate this approach using the example of the standard quantum mechanical simple harmonic oscillator.
