scholarly journals New types of solvability in PT symmetric quantum theory

2004 ◽  
pp. 333-347 ◽  
Author(s):  
Miloslav Znojil
Keyword(s):  
Quantum Theory ◽  
Symmetric Quantum

scholarly journals IS PT -SYMMETRIC QUANTUM THEORY FALSE AS A FUNDAMENTAL THEORY?

2016 ◽  
Vol 56 (3) ◽  
pp. 254 ◽  
Author(s):  
Miloslav Znojil
Keyword(s):  
Quantum Theory ◽  
Fundamental Theory ◽  
Model Based ◽  
Symmetric Quantum ◽  
Present Text ◽  
Recent Extension

Yi-Chan Lee et al. claim (cf. Phys. Rev. Lett. 112, 130404 (2014)) that the “recent extension of quantum theory to non-Hermitian Hamiltonians” (which is widely known under the nickname of “<em>PT</em>-symmetric quantum theory”) is “likely false as a fundamental theory”. By their opinion their results “essentially kill any hope of <em>PT</em>-symmetric quantum theory as a fundamental theory of nature”. In our present text we explain that their toy-model-based considerations are misleading and that they do not imply any similar conclusions.

scholarly journals Generation of families of spectra in PT -symmetric quantum mechanics and scalar bosonic field theory

2013 ◽  
Vol 371 (1989) ◽  
pp. 20120049 ◽  
Author(s):  
Steffen Schmidt ◽  
S. P. Klevansky
Keyword(s):  
Field Theory ◽  
Quantum Mechanics ◽  
Quantum Theory ◽  
Complex Analysis ◽  
One Dimension ◽  
Quantum Mechanical ◽  
Bosonic Field ◽  
Symmetric Quantum ◽  
The Difference ◽  
Do So

This paper explains the systematics of the generation of families of spectra for the -symmetric quantum-mechanical Hamiltonians H = p 2 + x 2 (i x ) ϵ , H = p 2 +( x 2 ) δ and H = p 2 −( x 2 ) μ . In addition, it contrasts the results obtained with those found for a bosonic scalar field theory, in particular in one dimension, highlighting the similarities to and differences from the quantum-mechanical case. It is shown that the number of families of spectra can be deduced from the number of non-contiguous pairs of Stokes wedges that display symmetry. To do so, simple arguments that use the Wentzel–Kramers–Brillouin approximation are used, and these imply that the eigenvalues are real. However, definitive results are in most cases presently only obtainable numerically, and not all eigenvalues in each family may be real. Within the approximations used, it is illustrated that the difference between the quantum-mechanical and the field-theoretical cases lies in the number of accessible regions in which the eigenfunctions decay exponentially. This paper reviews and implements well-known techniques in complex analysis and -symmetric quantum theory.

scholarly journals Uncertainty Relations: Curiosities and Inconsistencies

Symmetry ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 1640
Author(s):  
Krzysztof Urbanowski
Keyword(s):  
Quantum Theory ◽  
Lower Bound ◽  
Uncertainty Relation ◽  
Quantum Particle ◽  
Uncertainty Relations ◽  
Rigorous Analysis ◽  
Special Cases ◽  
The Status ◽  
Symmetric Quantum ◽  
Standard Deviations

Analyzing general uncertainty relations one can find that there can exist such pairs of non-commuting observables A and B and such vectors that the lower bound for the product of standard deviations ΔA and ΔB calculated for these vectors is zero: ΔA·ΔB≥0. Here we discuss examples of such cases and some other inconsistencies which can be found performing a rigorous analysis of the uncertainty relations in some special cases. As an illustration of such cases matrices (2×2) and (3×3) and the position–momentum uncertainty relation for a quantum particle in the box are considered. The status of the uncertainty relation in PT–symmetric quantum theory and the problems associated with it are also studied.

Conventional Bell Basis in PT-symmetric Quantum Theory

2018 ◽  
Vol 57 (12) ◽  
pp. 3839-3849
Author(s):  
Xiang-yu Zhu ◽  
Yuan-hong Tao
Keyword(s):  
Quantum Theory ◽  
Symmetric Quantum ◽  
Bell Basis

scholarly journals An algebraic PT-symmetric quantum theory with a maximal mass

2016 ◽  
Vol 47 (2) ◽  
pp. 135-156 ◽  
Author(s):  
V. N. Rodionov ◽  
G. A. Kravtsova
Keyword(s):  
Quantum Theory ◽  
Symmetric Quantum ◽  
Maximal Mass

scholarly journals Embedding, simulation and consistency ofPT-symmetric quantum theory

2018 ◽  
Vol 382 (36) ◽  
pp. 2578-2585 ◽  
Author(s):  
Minyi Huang ◽  
Asutosh Kumar ◽  
Junde Wu
Keyword(s):  
Quantum Theory ◽  
Symmetric Quantum

scholarly journals Anti-PT Transformations and Complex PT-Symmetric Superpartners

2021 ◽  
Author(s):  
Sehban Kartal ◽  
Taha Koohrokhi ◽  
Ali Mohammadi
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Inner Product ◽  
Quantum Mechanical ◽  
Probabilistic Interpretation ◽  
Quantum Mechanical System ◽  
Complex Conjugation ◽  
New Formalism ◽  
Shape Invariant ◽  
Symmetric Quantum

Abstract A quantum mechanical system with unbroken super-and parity-time (PT)-symmetry is derived and analyzed. Here, we propose a new formalism to construct the complex PT-symmetric superpartners by extending the additive shape invariant potentials to the complex domain. The probabilistic interpretation of a PT-symmetric quantum theory is correlated with the calculation of a new linear operator called the C operator, instead of complex conjugation in conventional quantum mechanics. At the present work, we introduce an anti-PT (A PT) conjugation to redefine a new version of the inner product without any additional considerations. This PT-supersymmetric quantum mechanics, satisfies essential requirements such as completeness, orthonormality as well as probabilistic interpretation.

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