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arXiv quant-ph/0507015quant-phhep-thmath-phmath.MP
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双正交量子系统

Biorthogonal Quantum Systems

Thomas Curtright, Luca Mezincescu

摘要:

PT对称量子力学的模型提供了双正交量子系统的例子。后者将PT对称模型的所有结构进行了推广,特别是在对偶空间的PT构造失败的情况下。对于H=(p+ v)^2+ \sum_{k>0} μ_{k}exp(ikx)形式的模型,我们给出了一些精确的结果.在一些非平凡的情况下,得到了等价的厄米理论,并证明是非常简单的:它们只是自由(手征)粒子。场论扩展被简要地考虑。

英文摘要:

Models of PT symmetric quantum mechanics provide examples of biorthogonal quantum systems. The latter incorporporate all the structure of PT symmetric models, and allow for generalizations, especially in situations where the PT construction of the dual space fails. The formalism is illustrated by a few exact results for models of the form H=(p+ν)^2+\sum_{k>0}μ_{k}exp(ikx). In some non-trivial cases, equivalent hermitian theories are obtained and shown to be very simple: They are just free (chiral) particles. Field theory extensions are briefly considered.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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