一维奇型Dirac算式自伴域的刻画

Self-adjoint domain of one-dimensional singular dirac operator

Dirac方程是量子力学的基本方程,讨论Dirac算式的自伴域在数学物理中有广泛的应用,文中根据Dirac算式的最大定义域、最小定义域和Dirac算式在区间[0,b]上的自伴域的结果,利用自伴延拓的Calkin描述通过对b取极限的讨论推导出Dirac算式在区间[0,+∞)上的自伴域D(T(L))={f∈D(L)|f1(0)cosα+f2(0)sinα},并证明了当势函数q1(x),q2(x)为区间[0,+∞)上的实值连续函数,则L必是极限点.

Dirac equation is one of the fundamental equations of quantum mechanics, and discussion of self-adjoint domains is very important in mathematics and physics. By using maximum and minimum independent variable of Dirac operator and the conclusions of regular Dirae operator＇s self-adjoint domains in [0 ,b], one dimensional singular Dirac operator＇s self-adjoint domains D（T（L） ） = {f∈ D（L）｜f1 （0）cos α ＋f2 （0）sin α }in [0, ＋∞ ） were described. It was concluded that singular dirac operator L was limit-point when the potential was continuous.