On the eigenproblems of PT-symmetric oscillators

被引:36
作者
Shin, KC [1 ]
机构
[1] Univ Illinois, Dept Math, Urbana, IL 61801 USA
基金
美国国家科学基金会;
关键词
D O I
10.1063/1.1366328
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
We consider the non-Hermitian Hamiltonian H=-d(2)/dx(2)+P(x(2))-(ix)(2n+1) on the real line, where P(x) is a polynomial of degree at most n greater than or equal to1 with all non-negative real coefficients (possibly P=0). It is proved that the eigenvalues lambda must be in the sector \arg lambda\less than or equal to pi/(2n+3). Also for the cubic case H=-d(2)/dx(2)-(ix)(3), we establish a zero-free region of the eigenfunction u and its derivative u' and we find some other interesting properties of eigenfunctions. (C) 2001 American Institute of Physics.
引用
收藏
页码:2513 / 2530
页数:18
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