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Applied Mathematics-A Journal of Chinese Universities  2019, Vol. 34 Issue (2): 173-    DOI: 10.1007/s11766-017-3568-6
    
The geometrical properties of parity and time reversal operators in two dimensional spaces
HUANG Min-yi, YANG Yu, WU Jun-de, CHO Min-Hyung
1 School of Mathematical Science, Zhejiang University, Hangzhou 310027, People’s Republic of China.
2 Department of Mathematics, National University of Singapore, Singapore 119076, Republic of Singapore.
3 Department of Applied Mathematics, Kumoh National Institute of Technology, Kyungbuk, 39177,Korea.
The geometrical properties of parity and time reversal operators in two dimensional spaces
HUANG Min-yi, YANG Yu, WU Jun-de, CHO Min-Hyung
1 School of Mathematical Science, Zhejiang University, Hangzhou 310027, People’s Republic of China.
2 Department of Mathematics, National University of Singapore, Singapore 119076, Republic of Singapore.
3 Department of Applied Mathematics, Kumoh National Institute of Technology, Kyungbuk, 39177,Korea.
 全文: PDF 
摘要： The parity operator P and time reversal operator T are two important operators in
the quantum theory, in particular, in the PT -symmetric quantum theory. By using the concrete
forms of P and T , we discuss their geometrical properties in two dimensional spaces. It is showed
that if T is given, then all P links with the quadric surfaces; if P is given, then all T links with
the quadric curves. Moreover, we give out the generalized unbroken PT -symmetric condition of
an operator. The unbroken PT -symmetry of a Hermitian operator is also showed in this way.
关键词： PT -symmetry;  geometrical property;  unbroken condition    
Abstract: The parity operator P and time reversal operator T are two important operators in
the quantum theory, in particular, in the PT -symmetric quantum theory. By using the concrete
forms of P and T , we discuss their geometrical properties in two dimensional spaces. It is showed
that if T is given, then all P links with the quadric surfaces; if P is given, then all T links with
the quadric curves. Moreover, we give out the generalized unbroken PT -symmetric condition of
an operator. The unbroken PT -symmetry of a Hermitian operator is also showed in this way.
Key words: PT -symmetry    geometrical property    unbroken condition
出版日期: 2019-07-03
CLC:  47B37  
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HUANG Min-yi
YANG Yu
WU Jun-de
CHO Min-Hyung

引用本文:

HUANG Min-yi, YANG Yu, WU Jun-de, CHO Min-Hyung. The geometrical properties of parity and time reversal operators in two dimensional spaces[J]. Applied Mathematics-A Journal of Chinese Universities, 2019, 34(2): 173-.

HUANG Min-yi, YANG Yu, WU Jun-de, CHO Min-Hyung. The geometrical properties of parity and time reversal operators in two dimensional spaces. Applied Mathematics-A Journal of Chinese Universities, 2019, 34(2): 173-.

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http://www.zjujournals.com/amjcub/CN/ 10.1007/s11766-017-3568-6    或    http://www.zjujournals.com/amjcub/CN/Y2019/V34/I2/173

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