Introduction to PT-symmetric quantum theory

被引:360
|
作者
Bender, CM
机构
[1] Univ London Imperial Coll Sci Technol & Med, Blackett Lab, London SW7 2BZ, England
[2] Washington Univ, Dept Phys, St Louis, MO 63130 USA
基金
英国工程与自然科学研究理事会;
关键词
D O I
10.1080/00107500072632
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
In most introductory courses on quantum mechanics one is taught that the Hamiltonian operator must be Hermitian in order that the energy levels be real and that the theory be unitary (probability conserving). To express the Hermiticity of a Hamiltonian, one writes H=H dagger, where the symbol dagger denotes the usual Dirac Hermitian conjugation; that is, transpose and complex conjugate. In the past few years it has been recognized that the requirement of Hermiticity, which is often stated as an axiom of quantum mechanics, may be replaced by the less mathematical and more physical requirement of space-time reflection symmetry (PT symmetry) without losing any of the essential physical features of quantum mechanics. Theories defined by non-Hermitian PT-symmetric Hamiltonians exhibit strange and unexpected properties at the classical as well as at the quantum level. This paper explains how the requirement of Hermiticity can be evaded and discusses the properties of some non-Hermitian PT-symmetric quantum theories.
引用
收藏
页码:277 / 292
页数:16
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