d维量子力学问题正弦基的宽有效性
Wide effectiveness of a sine basis for quantum-mechanical problems in d dimensions
摘要：
证明了由量子力学中盒中粒子的本征函数{sqrt{2} sin（nπx）}_{n=1}^{ \infty }提供的L^2（[0，1]）的生成集为更一般的问题提供了一个非常有效的变分基.基被缩放到[a，b]，其中a和b然后被用作变分参数。对于被限制在R^d中的球盒中的量子系统来说，这也许是一个自然的基础，但结果证明它也适用于被U形势软限制的问题，包括那些在r=0处具有强奇点的问题。具体的例子进行了详细讨论，随着一些束缚N-玻色子系统
英文摘要：
It is shown that the spanning set for L^2([0, 1]) provided by the eigenfunctions {sqrt{2} sin(nπx)}_{n=1}^{\infty} of the particle-in-a-box in quantum mechanics provide a very effective variational basis for more general problems. The basis is scaled to [a,b], where a and b are then used as variational parameters. What is perhaps a natural basis for quantum systems confined to a spherical box in R^d, turns out to be appropriate also for problems that are softly confined by U-shaped potentials, including those with strong singularities at r=0. Specific examples are discussed in detail, along with some bound N-boson systems
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