scholarly journals Alternating Coordinate-Momentum Representation for Quantum States Based on Bopp Operators for Modelling Long-Distance Coherence Aspects

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Ezzat G. Bakhoum ◽  
Cristian Toma
Keyword(s):  
Wave Train ◽  
Linear Equations ◽  
Quantum States ◽  
Wave Functions ◽  
Momentum Representation ◽  
Long Distance ◽  
Support Functions ◽  
Vector Potentials ◽  
Time Origin ◽  
Good Manner

This study presents an alternating coordinate-momentum representation for propagation and transition of associated wave function, based on Bopp operators and on a certain symbolic determinant corresponding to a set of two linear equations with null free terms. It is shown that this alternating representation can justify in a good manner the patterns created through reflection/refraction of waves on nonperfectly smooth interfaces and phase correspondence of diffracted beams without the need of supplementary support functions. Correlations with Lorentz transformation of wave functions by interaction with a certain material medium (the space-time origin of a wave-train being adjusted) are also presented, and supplementary aspects regarding the use of electromagnetic scalar and vector potentials for modelling evolution within this alternating representation are added.

Quantum Theory

2017 ◽  
Author(s):  
Frank S. Levin
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Uncertainty Principle ◽  
Quantum Spin ◽  
Quantum States ◽  
Wave Functions ◽  
Symbolic Representations ◽  
Quantum Numbers ◽  
The Subject ◽  
Heisenberg's Uncertainty Principle

The subject of Chapter 8 is the fundamental principles of quantum theory, the abstract extension of quantum mechanics. Two of the entities explored are kets and operators, with kets being representations of quantum states as well as a source of wave functions. The quantum box and quantum spin kets are specified, as are the quantum numbers that identify them. Operators are introduced and defined in part as the symbolic representations of observable quantities such as position, momentum and quantum spin. Eigenvalues and eigenkets are defined and discussed, with the former identified as the possible outcomes of a measurement. Bras, the counterpart to kets, are introduced as the means of forming probability amplitudes from kets. Products of operators are examined, as is their role underpinning Heisenberg’s Uncertainty Principle. A variety of symbol manipulations are presented. How measurements are believed to collapse linear superpositions to one term of the sum is explored.

Long distance two-party quantum crypto made simple

2012 ◽  
Vol 12 (5&6) ◽  
pp. 448-460
Author(s):  
Iordanis Kerenidis ◽  
Stephanie Wehner
Keyword(s):  
Quantum Communication ◽  
Oblivious Transfer ◽  
Difficult Problem ◽  
Entanglement Swapping ◽  
Quantum States ◽  
Large Network ◽  
Long Distance ◽  
Computational Problem ◽  
Cryptographic Primitive

Any two-party cryptographic primitive can be implemented using quantum communication under the assumption that it is difficult to store a large number of quantum states perfectly. However, achieving reliable quantum communication over long distances remains a difficult problem. Here, we consider a large network of nodes with only neighboring quantum links. We exploit properties of this cloud of nodes to enable any two nodes to achieve security even if they are not directly connected. Our results are based on techniques from classical cryptography and do not resort to technologically difficult procedures like entanglement swapping. More precisely, we show that oblivious transfer can be achieved in such a network if and only if there exists a path in the network between the sender and the receiver along which all nodes are honest. Finally, we show that useful notions of security can still be achieved when we relax the assumption of an honest path. For example, we show that we can combine our protocol for oblivious transfer with computational assumptions such that we obtain security if either there exists an honest path, or, as a backup, at least the adversary cannot solve a computational problem.

scholarly journals Quarks im Lichte einer Idee von Pais

1980 ◽  
Vol 35 (2) ◽  
pp. 252-253
Author(s):  
Fritz Bopp
Keyword(s):  
Wave Equation ◽  
Infinite Sequence ◽  
Quantum States ◽  
Wave Functions ◽  
Exclusion Principle ◽  
Repulsive Forces

Abstract A wave equation of a kind proposed by Pais in 1953 describes a particle with an infinite sequence of quantum states, which belong to the symmetrical representations (λ, 0) of the group SU 3. Particles composed of such single ones are connected with the whole set of representations (λ, μ) of SU 3. The wave equation is compatible with an exclusion principle. Assuming that only particles with zero triality occur, all quarks and quarklike particles are excluded. Neither coulours, nor bags are needed, as we do not need repulsive forces to exclude Li-atoms with symmetrical wave functions.

scholarly journals The Strange (Hi)story of Particles and Waves

2016 ◽  
Vol 71 (3) ◽  
pp. 195-212
Author(s):  
H. Dieter Zeh
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Quantum Theory ◽  
Excited States ◽  
Configuration Space ◽  
Historical Context ◽  
Quantum States ◽  
Wave Functions ◽  
General Readership ◽  
Boson Fields

AbstractThis is an attempt of a non-technical but conceptually consistent presentation of quantum theory in a historical context. While the first part is written for a general readership, Section 5 may appear a bit provocative to some quantum physicists. I argue that the single-particle wave functions of quantum mechanics have to be correctly interpreted as field modes that are “occupied once” (i.e. first excited states of the corresponding quantum oscillators in the case of boson fields). Multiple excitations lead to apparent many-particle wave functions, while the quantum states proper are defined by wave function(al)s on the “configuration” space of fundamental fields, or on another, as yet elusive, fundamental local basis.

MACROSCOPICITY AND CLASSICALITY OF QUANTUM FLUCTUATIONS IN DE SITTER SPACE

1988 ◽  
Vol 03 (10) ◽  
pp. 929-940 ◽  
Author(s):  
SUMIO WADA
Keyword(s):  
Quantum Mechanics ◽  
Quantum Fluctuations ◽  
Quantum States ◽  
Wave Functions ◽  
Interpretation Of Quantum Mechanics ◽  
De Sitter Spacetime ◽  
Probabilistic Interpretation ◽  
De Sitter ◽  
Sitter Spacetime ◽  
Matter Fields

On the basis of the non-probabilistic interpretation of quantum mechanics, we define “macroscopicity” and “classicality” of quantum fluctuations as closely related but separate concepts. Then these properties are examined in quantum states (wave functions) of matter fields in de Sitter spacetime.

EXACT QUANTUM STATES OF AN INVERTED PENDULUM UNDER TIME-DEPENDENT GRAVITATION

2004 ◽  
Vol 19 (24) ◽  
pp. 4165-4172 ◽  
Author(s):  
I. A. PEDROSA ◽  
I. GUEDES
Keyword(s):  
Exact Solutions ◽  
Inverted Pendulum ◽  
Quantum States ◽  
Wave Functions ◽  
Time Dependent ◽  
Invariant Method ◽  
Exact Quantum ◽  
Generalized Time

We discuss the Lewis and Riesenfeld invariant method for cases where the invariant has continuous eigenvalues and use it to find the Schrödinger wave functions of an inverted pendulum under time-dependent gravitation. As a particular case, we consider an inverted pendulum with exponentially increasing mass and constant gravitation. We also obtain the exact solutions for a generalized time-dependent inverted pendulum.

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