关于与-y“（x）+（-1）^nx ^{2n}y（x）相关的PT对称算子的域
On Domains of PT Symmetric Operators Related to -y''(x) + (-1)^n x^{2n}y(x)
摘要：
近年来，人们利用谐振子哈密顿量的复变形H=p^2 +x^2（ix）^ε研究了厄米性的推广，其中ε是实参数。这些复哈密顿量具有PT对称性（宇称和时间反演的乘积），可以具有实谱。我们将考虑最简单的情况：εeven。本文描述了与H=p^2 +x^2（ix）^ε相关的所有自伴（Hermitian）同时又是PT对称的算子。令人惊讶的是，有一大类与H=p^2 +x^2（ix）^ε相关的自伴算子不是PT对称的。
英文摘要：
In the recent years a generalization of Hermiticity was investigated using a complex deformation H=p^2 +x^2(ix)^εof the harmonic oscillator Hamiltonian, where εis a real parameter. These complex Hamiltonians, possessing PT symmetry (the product of parity and time reversal), can have real spectrum. We will consider the most simple case: εeven. In this paper we describe all self-adjoint (Hermitian) and at the same time PT symmetric operators associated to H=p^2 +x^2(ix)^ε. Surprisingly it turns out that there are a large class of self-adjoint operators associated to H=p^2 +x^2(ix)^εwhich are not PT symmetric.
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