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Real eigenvalues determined by recursion of eigenstates |
| Tong Liu(刘通) and Youguo Wang(王友国)† |
| School of Science, Nanjing University of Posts and Telecommunications, Nanjing 210003, China |
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Abstract Quantum physics is primarily concerned with real eigenvalues, stemming from the unitarity of time evolutions. With the introduction of PT symmetry, a widely accepted consensus is that, even if the Hamiltonian of the system is not Hermitian, the eigenvalues can still be purely real under specific symmetry. Hence, great enthusiasm has been devoted to exploring the eigenvalue problem of non-Hermitian systems. In this work, from a distinct perspective, we demonstrate that real eigenvalues can also emerge under the appropriate recursive condition of eigenstates. Consequently, our findings provide another path to extract the real energy spectrum of non-Hermitian systems, which guarantees the conservation of probability and stimulates future experimental observations.
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Received: 22 September 2023
Revised: 11 December 2023
Accepted manuscript online: 20 December 2023
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PACS:
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03.65.Aa
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(Quantum systems with finite Hilbert space)
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| Fund: This work was supported by the National Natural Science Foundation of China (Grant No. 62071248), the Natural Science Foundation of Nanjing University of Posts and Telecommunications (Grant No. NY223109), and China Postdoctoral Science Foundation (Grant No. 2022M721693). |
Corresponding Authors:
Youguo Wang
E-mail: wangyg@njupt.edu.cn
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Cite this article:
Tong Liu(刘通) and Youguo Wang(王友国) Real eigenvalues determined by recursion of eigenstates 2024 Chin. Phys. B 33 030303
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