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Construction of C operator for a PT symmetric model

Rajkumar Roychoudhury, Pinaki Roy

We obtain closed form expression of the C(x,y) operator for the PT symmetric Scarf I potential. It is also shown that the eigenfunctions are complete.

arXiv:0705.4376Journal of Physics A Mathematical and TheoreticalMay 30, 20070 citations

On the construction and solution of -symmetric models

J. Gruneberg

Nuclear Physics BMar 1, 200010 citations

Spectrum of the Metric Operator of a Simple -Symmetric Model

Jakub Železný

International Journal of Theoretical PhysicsDec 21, 20104 citations

The representation and construction of C in CPT -frame

Wenhua Wang, Wen-ting Liang, Zhengli Chen

Abstract The rigorous definition of appropriate inner products for quantum systems governed by PT -symmetric Hamiltonians H necessitates the fundamental construction of a time-independent observable operator C , central to ensuring physical consistency in such frameworks. This investigation focuses on the structural characteristics and operational significance of the C operator within the PT -symmetric quantum framework established through the mathematical foundations of CPT symmetry. We establish that within a CPT -symmetry framework, the operator C can be expressed as the exponential of a Hermitian operator Q , multiplied by the parity operator P . Leveraging the geometric properties inherent to the Krein space, we proceed to reconstruct the operator C for a precisely solvable PT -symmetric Hamiltonian within an L 2 ( − π , π ) model.Abstract The rigorous definition of appropriate inner products for quantum systems governed by PT -symmetric Hamiltonians H necessitates the fundamental construction of a time-independent observable operator C , central to ensuring physical consistency in such frameworks. This investigation focuses on the structural characteristics and operational significance of the C operator within the PT -symmetric quantum framework established through the mathematical foundations of CPT symmetry. We establish that within a CPT -symmetry framework, the operator C can be expressed as the exponential of a Hermitian operator Q , multiplied by the parity operator P . Leveraging the geometric properties inherent to the Krein space, we proceed to reconstruct the operator C for a precisely solvable PT -symmetric Hamiltonian within an L 2 ( − π , π ) model.

Laser Physics LettersApr 1, 20250 citations

Investigation of PT -symmetric Hamiltonian Systems from an Alternative Point of View

Junqing Li, Qian Li, Yan-Gang Miao

Two non-Hermitian PT-symmetric Hamiltonian systems are reconsidered by means of the algebraic method which was originally proposed for the pseudo-Hermitian Hamiltonian systems rather than for the PT-symmetric ones. Compared with the way converting a non-Hermitian Hamiltonian to its Hermitian counterpart, this method has the merit that keeps the Hilbert space of the non-Hermitian PT-symmetric Hamiltonian unchanged. In order to give the positive definite inner product for the PT-symmetric systems, a new operator V, instead of C, can be introduced. The operator V has the similar function to the operator C adopted normally in the PT-symmetric quantum mechanics, however, it can be constructed, as an advantage, directly in terms of Hamiltonians. The spectra of the two non-Hermitian PT-symmetric systems are obtained, which coincide with that given in literature, and in particular, the Hilbert spaces associated with positive definite inner products are worked out.Two non-Hermitian PT-symmetric Hamiltonian systems are reconsidered by means of the algebraic method which was originally proposed for the pseudo-Hermitian Hamiltonian systems rather than for the PT-symmetric ones. Compared with the way converting a non-Hermitian Hamiltonian to its Hermitian counterpart, this method has the merit that keeps the Hilbert space of the non-Hermitian PT-symmetric Hamiltonian unchanged. In order to give the positive definite inner product for the PT-symmetric systems, a new operator V, instead of C, can be introduced. The operator V has the similar function to the operator C adopted normally in the PT-symmetric quantum mechanics, however, it can be constructed, as an advantage, directly in terms of Hamiltonians. The spectra of the two non-Hermitian PT-symmetric systems are obtained, which coincide with that given in literature, and in particular, the Hilbert spaces associated with positive definite inner products are worked out.

arXiv:1204.6544Communications in Theoretical PhysicsOct 1, 201213 citations

The Weyl Operator and its Generalization

Leon W. Cohen

Springer eBooksDec 11, 201277 citations

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