典型非自连接的 Schroedinger 操作符的特征功能近似值
On eigenfunction approximations for typical non-self-adjoint Schroedinger operators
A. Aslanyan and E. B. Davies
arXiv
1999年4月19日
我们在一个维度上为非自连接的 Schroedinger 运算符的特征函数构建高效的近似值。 同样的想法也适用于具有扩张分析潜力的自我相邻的Schroedinger运算符的共振研究。 尽管这种特征函数具有令人惊讶的复杂结构,具有多个局部最大值,但我们表明,JWKB方法的合适调整能够为他们提供准确的横向近似。
We construct efficient approximations for the eigenfunctions of non-self-adjoint Schroedinger operators in one dimension. The same ideas also apply to the study of resonances of self-adjoint Schroedinger operators which have dilation analytic potentials. In spite of the fact that such eigenfunctions can have surprisingly complicated structures with multiple local maxima, we show that a suitable adaptation of the JWKB method is able to provide accurate lobal approximations to them.