Extending Quantum Probability from Real Axis to Complex Plane

Yang, Ciann Dong; Han, Shiang-Yi

doi:10.3390/e23020210

Cited by 10 publications

(11 citation statements)

References 45 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This definition ensures finite norms of the wave functions. It corresponds to an extension of the concept of probability in the complex plane [15]. Note that the cos term oscillates rapidly as the phase function becomes large.…”

Section: Sketching the Methodsmentioning

confidence: 99%

PT-symmetry rules applied to a class of real potentials

Garidi,

Lombard,

Mezhoud

2024

Phys. Scr.

View full text Add to dashboard Cite

Extending the functional space to complex eigenfunctions [1], we have shown that infinitely negative potentials at large distances admit finite energy states. The used techniques are similar to the ones applied in the case of PT symmetric complex potentials with real eigenvalues. We present the lowest part of the spectra for −|x|n potentials with 4 ≤ n ≤ 8. We also discuss the norm and orthogonalities of the wave functions.

show abstract

Section: Sketching the Methodsmentioning

confidence: 99%

PT-symmetry rules applied to a class of real potentials

Garidi,

Lombard,

Mezhoud

2024

Phys. Scr.

View full text Add to dashboard Cite

show abstract

“…Newman has also speculated about this [6]. Complex space methods have been proposed and applied in Bohmian and stochastic mechanics [34]. The wormholes of general relativity are related to complex space-time by the Kerr-Schild metric construction.…”

Section: Ods In Physicsmentioning

confidence: 99%

Classical Charged Particle Models Derived from Complex Shift Methods

Davidson

2023

Int J Theor Phys

View full text Add to dashboard Cite

Extended charged objects embedded in complex space-time are proposed using the double-copy or complex shift method. Most of the objects studied are 3D strings in dierent shapes. The most detailed case studied is a static-charged open string. It is found that this can be interpreted purely electromagnetically. It exhibits the same relation between charge, mass, angular momentum, and magnetic moment as the Dirac equation and the Kerr-Newman metric. The spin of the particle is purely electromagnetic, as is the mass. A gyromagnetic ratio of 2 is obtained. The elds in this case are multi-valued, and the singular part of the elds can be arranged to be on an unphysical Riemann sheet with a judicious selection of Riemann cut surfaces. The calculations of mass and angular momentum are done numerically using multi-precision algorithms included as a Python script. The mass calculation agrees with the measured electron mass. Particles for knotted or linked strings in 3 space dimensions are also proposed, and these inherit the topological invariants of the knot or link they are based on. A liquid drop model with complex shift is also discussed. The multi-valued behavior of the solutions, related to that of the Kerr-Newman metric, can be thought of as the origin of the Einstein-Rosen bridge, and the conjectures that this is the origin of quantum entanglement, ER=EPR, is therefore supported in this theory. So we have here a classical theory that has some properties of quantum mechanics. Hopefully it can oer a new phenomenological application of string theory as a semiclassical model for elementary particles, nuclei, and solitons in condensed matter, uids, and gases.

show abstract

“…In Reference [ 36 ], the application of quantum information and field theories to modeling of social process is done. In Reference [ 37 ], the probability domain was extended to the complex space, and the relation of the complex probabilities to the quantum probabilities was obtained. The relation between the quantum state description and the classical state description is elucidated in References [ 26 , 38 , 39 , 40 ].…”

Section: Introductionmentioning

confidence: 99%

Probability Representation of Quantum States

Манько

Man’ko

2021

Entropy

View full text Add to dashboard Cite

The review of new formulation of conventional quantum mechanics where the quantum states are identified with probability distributions is presented. The invertible map of density operators and wave functions onto the probability distributions describing the quantum states in quantum mechanics is constructed both for systems with continuous variables and systems with discrete variables by using the Born’s rule and recently suggested method of dequantizer–quantizer operators. Examples of discussed probability representations of qubits (spin-1/2, two-level atoms), harmonic oscillator and free particle are studied in detail. Schrödinger and von Neumann equations, as well as equations for the evolution of open systems, are written in the form of linear classical–like equations for the probability distributions determining the quantum system states. Relations to phase–space representation of quantum states (Wigner functions) with quantum tomography and classical mechanics are elucidated.

show abstract

Extending Quantum Probability from Real Axis to Complex Plane

Cited by 10 publications

References 45 publications

PT-symmetry rules applied to a class of real potentials

PT-symmetry rules applied to a class of real potentials

Classical Charged Particle Models Derived from Complex Shift Methods

Probability Representation of Quantum States

Contact Info

Product

Resources

About