Variational Principle for a Particle in a Box
Variational Principle for a Particle in a Box
复制标题
盒子中粒子的变分原理
DOI：
10.1021/ed077p1221
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发表时间：
2000
影响因子：
3
通讯作者：
G. Doggett
中科院分区：
文献类型：
--
作者：
J. I. Casaubon;G. Doggett
使用不同的模型波函数，重新检查盒子中的粒子问题，以说明使用变分原理应用于最简单的可解量子力学问题。该方案为LCAO方法在原子和分子计算中的应用提供了一个有用的范例。合适的多项式基函数的引入，提供了一种方法，用于控制的精度和数量的独立变分参数中使用的能量计算，当坐标原点是在左手边或中心的方块。链接与Bransden和Joachain计算的前两个甚至宇称状态。近似的基态波函数，x（x-L），也被重新定义，通过引入一个变化参数的形式的处方的基础上的位置坐标的值。最后，提出了一种简单的方法，用于确定一个任意的激发态的近似能量，基于使用任何应用程序…
The particle-in-a-box problem is reexamined, using different model wave functions, to illustrate the use of the variational principle applied to the simplest solvable quantum mechanical problem. The scheme presented here provides a useful paradigm for the LCAO approach used in atomic and molecular calculations. Suitable polynomial basis functions are introduced that provide a way for controlling both the accuracy and the number of independent variational parameters used in the energy calculations, when the coordinate origin is taken either at the left-hand edge or the center of the box. Links with the Bransden and Joachain calculations on the first two even parity states are made. The approximate ground state wave function, x(x - L), is also redefined by introducing a variation parameter in the form of a prescription based on the value of the position coordinate. Finally, a straightforward method is presented for determining an approximate energy for an arbitrary excited state, based on the use of any app...