Simplified theory of wavefunctions for homogeneous anisotropic media 均匀各向异性媒质的简化波函数理论
For a square quantum wire with finite barriers, there are three kinds of wavefunctions used formerly as follows : 1 对有限深方形量子线,前人所取波函数主要有三种形式,总结如下:1
Abstract : the wavefunctions and energy eigenvalues for the ring-shaped oscillator are obtained using the ideas of supersymmetric quantum mechanics and shape invaricace 文摘:采用量子力学中的超对称性和形不变性,讨论环形振子的波函数和能量本征值
The basic idea is that when a quantum system interacts with a measuring apparatus, their respective wavefunctions become entangled, so that the original quantum system ceases to exist as an independent entity 基本的思想就是当一个量子系统互相与测量仪器作用时候,它们各自波函数变得纠缠,因此最初量子系统终结了以一独立实体存在。
Normalized radial wavefunctions of the ring-shaped oscillator have been obtained in ref . 1 . on the basis of previous works , in this paper , the general formulas and the recurrence formulas for radial matrix elements of the ring-shaped oscillator are derived 利用文献1给出的环形振子的归一化的径向波函数,推导出环形振子径向矩阵元的通项表达式及其递推关系.解决了环形振子径向矩阵元的计算问题
In fact, the deep overlapping of the wavepacket of particles implies new interactions which are technically called nonlinear ( in the sense of depending on powers of the wavefunctions bigger than one ), nonlocal ( in the sense that they are extended over the volume of wave-overlappings which cannot be evidently reduced to finite number of isolated points ), as well as nonpotential ( in the sense of being of contact / zero { range type for which the notion of action-at-a-distance potential has no mathematical or physical meaning of any type } 事实上,粒子相互之间深深重叠的波包意味着新型的相互作用,技术上它可称之为非线性意义为它们取决于波函数大于1次的幕而定,为非局部意义为它们的延伸超越了波重叠的体积,使其显然无法再缩小到有限数孤立点,以及为非潜能意义为相互接触零距离,在这种情况下一定距离下作用的潜势不再有任何数学上或物理上的意义。
But difficulty in maths will come forth when meeting high spin particles if we using such method . on base of the characteristic of energy space, we obtained the wavefunctions and geometric phase by the trial function method in this paper . the berry phase of the system are also obtained after an evolution period 文中在绝热近似下根据自旋粒子能级间隔特点用尝试波函数法求出了旋转磁场中高自旋粒子系统的波函数及几何相位,解决了用一般方法求解时出现高阶微分方程的困难。
From discussing and analyzing the calculated outcome we obtain the conclusions as follows : 1 . for the energies of the single electron in a square quantum wire with finite barriers, the former wavefunctions [ 12-14 ] are only available to the wide wires . for the oscillator strength of the single electron in a square quantum wire with finite barriers, the former wavefunctions are not appropriate 通过对计算结果的讨论和分析,得到以下结论:1.对有限深方形量子线中单电子的基态能和第一激发态能,前人’2一’‘’所取波函数只适合计算宽阱时的情况,对有限深方形量子线中单
From discussing and analyzing the calculated outcome we obtain the conclusions as follows : 1 . for the energies of the single electron in a square quantum wire with finite barriers, the former wavefunctions [ 12-14 ] are only available to the wide wires . for the oscillator strength of the single electron in a square quantum wire with finite barriers, the former wavefunctions are not appropriate 通过对计算结果的讨论和分析,得到以下结论:1.对有限深方形量子线中单电子的基态能和第一激发态能,前人’2一’‘’所取波函数只适合计算宽阱时的情况,对有限深方形量子线中单
The first two kinds of wavefunctions are simple formally, but there must be error of the numerical values of some physical magnitudes because there is a trouble with the continuity of the function and of its derivative divided by the band-mass at the boundaries . though the third kind of wavefunction can satisfy the continuity of the function and of its derivative divided by the band-mass, the number of the terms is so large that it is difficult to calculate the physical magnitudes in the single quantum wire 前两种波函数形式比较简单,但由于在边界处波函数的河北师范大学硕士学位论文连续性条件和粒子流的守恒条件存在问题,这必将对某些物理量的计算产生影响;第三种波函数在边界处满足波函数的连续性条件和粒子流的守恒条件,但是对于单量子线需要展开的项数很多,计算量太大。