scholarly journals DIFFRACTION EXPERIMENTS WITH KOSSEL PHOTONS

2021 ◽  
Vol 58 ◽  
pp. 3-10
Author(s):  
Oleg P. Nikotin ◽  
Keyword(s):  
Quantum Mechanics ◽  
Energy Resolution ◽  
Wave Functions ◽  
Coordinate Space ◽  
Diffraction Scattering ◽  
Sense Data ◽  
Space Experiments ◽  
Measurement Results ◽  
Angular Measurements ◽  
Spatial Parameters

In the paper an attempt was made to obtain some information about the characteristics of photons as separate objects with the properties of localization in ordinary coordinate space. Experiments of various complexity with Kossel photons were carried out on a multiaxial diffractometer. A diffraction spectrometer with perfect calcite crystals was used to register the photons. The bidirectional angular measurements were carried out with sufficient angular and energy resolution to detect the influence of the coherent volume of the photons on the measurement results. The measurements showed some correlations that had not been paid enough attention before. Those effects were measured separately for Kα1 and Kα2 photons to allow their comparison. Such approach corresponds to the modern quantum mechanics of the photon; that mechanics showed the possibility of existence of wave functions of photons in their usual standard sense. Data on spatial parameters Kα1 and Kα2 of Kossel photons were obtained by comparing the effects of their diffraction scattering

scholarly journals On the Boundary Conditions in Deformed Quantum Mechanics with Minimal Length Uncertainty

2013 ◽  
Vol 2013 ◽  
pp. 1-4 ◽  
Author(s):  
Pouria Pedram
Keyword(s):  
Quantum Mechanics ◽  
Boundary Conditions ◽  
Adjoint Representation ◽  
Minimal Length ◽  
Wave Functions ◽  
Coordinate Space ◽  
Space Wave

We find the coordinate space wave functions, maximal localization states, and quasiposition wave functions in a GUP framework that implies a minimal length uncertainty using a formally self-adjoint representation. We show how the boundary conditions in quasiposition space can be exactly determined from the boundary conditions in coordinate space.

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.

A Student's Guide to the Schrödinger Equation

2020 ◽  
Author(s):  
Daniel A. Fleisch
Keyword(s):  
Quantum Mechanics ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Wave Functions ◽  
Plain Language ◽  
Science And Engineering ◽  
Popular Approach ◽  
Matlab Code ◽  
Mathematical Techniques

Quantum mechanics is a hugely important topic in science and engineering, but many students struggle to understand the abstract mathematical techniques used to solve the Schrödinger equation and to analyze the resulting wave functions. Retaining the popular approach used in Fleisch's other Student's Guides, this friendly resource uses plain language to provide detailed explanations of the fundamental concepts and mathematical techniques underlying the Schrödinger equation in quantum mechanics. It addresses in a clear and intuitive way the problems students find most troublesome. Each chapter includes several homework problems with fully worked solutions. A companion website hosts additional resources, including a helpful glossary, Matlab code for creating key simulations, revision quizzes and a series of videos in which the author explains the most important concepts from each section of the book.

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.

WKB method for potentials unbounded from below

2016 ◽  
Vol 30 (03) ◽  
pp. 1650003 ◽  
Author(s):  
Aleksandar Demić ◽  
Vitomir Milanović ◽  
Jelena Radovanović ◽  
Milenko Musić
Keyword(s):  
Quantum Mechanics ◽  
Bound States ◽  
Wave Functions ◽  
Wkb Method ◽  
Symmetric Potential ◽  
Overlap Integral ◽  
Entire Spectrum ◽  
One Dimensional ◽  
Model Based ◽  
Exactly Solvable

Bound states degenerated in energy (and differing in parity) may form in one-dimensional quantum mechanics if the potential is unbounded from below. We focus on symmetric potential and present quasi-exactly solvable (QES) model based on WKB method. The application of this method is limited on slow-changing potentials. We consider the overlap integral of WKB wave functions [Formula: see text] and [Formula: see text] which correspond to energies [Formula: see text] and [Formula: see text], and by setting [Formula: see text], we determine the type of spectrum depending on parameter [Formula: see text] which arises from this method. For finite value [Formula: see text], we show that the entire spectrum will consist of degenerated bound states.

scholarly journals Experimental Study on RFID Antenna Reading Areas in a Tunnel System

2017 ◽  
Vol 2017 ◽  
pp. 1-15
Author(s):  
Kai Kordelin ◽  
Jaana Kordelin ◽  
Markku Johansson ◽  
Johanna Virkki ◽  
Leena Ukkonen ◽  
...  
Keyword(s):  
Monitoring System ◽  
Nuclear Waste ◽  
Research Area ◽  
Diffraction Scattering ◽  
Nuclear Waste Storage ◽  
Waste Storage ◽  
Measurement Results ◽  
Radiofrequency Identification ◽  
Tunnel System ◽  
Antenna Location

We study optimized antenna reading area mappings for a radiofrequency identification- (RFID-) based access monitoring system, used in an underground nuclear waste storage facility. We shortly introduce the access monitoring system developed for the ONKALO tunnel in Finland and describe the antenna mounting points as well as the research area. Finally, we study the measurement results of the antenna reading areas and factors that affect the reading area size. Based on our results, in addition to antenna location and direction, absorption to obstacles, reflections, diffraction, scattering, and refraction affect the antenna reading area.

scholarly journals Quantum SU(2|1) supersymmetric ℂN Smorodinsky-Winternitz system

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Evgeny Ivanov ◽  
Armen Nersessian ◽  
Stepan Sidorov
Keyword(s):  
Quantum Mechanics ◽  
Energy Levels ◽  
Wave Functions ◽  
Supersymmetric Extension ◽  
Quantum Properties ◽  
Hidden Symmetry ◽  
Euclidian Space ◽  
Symmetry Operators ◽  
Symmetry Generators ◽  
Equivalent Description

Abstract We study quantum properties of SU(2|1) supersymmetric (deformed $$ \mathcal{N} $$ N = 4, d = 1 supersymmetric) extension of the superintegrable Smorodinsky-Winternitz system on a complex Euclidian space ℂN. The full set of wave functions is constructed and the energy spectrum is calculated. It is shown that SU(2|1) supersymmetry implies the bosonic and fermionic states to belong to separate energy levels, thus exhibiting the “even-odd” splitting of the spectra. The superextended hidden symmetry operators are also defined and their action on SU(2|1) multiplets of the wave functions is given. An equivalent description of the same system in terms of superconformal SU(2|1, 1) quantum mechanics is considered and a new representation of the hidden symmetry generators in terms of the SU(2|1, 1) ones is found.

EPR Elements of Physical Reality in Quantum Mechanics

1997 ◽  
Vol 12 (29) ◽  
pp. 5289-5303
Author(s):  
V. K. Thankappan ◽  
Ravi K. Menon
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Singlet State ◽  
Physical Reality ◽  
The State ◽  
Wave Functions ◽  
Definition Of

The concept of elements of physical reality (e.p.r.) in quantum mechanics as defined by Einstein, Podolsky and Rosen (EPR) is discussed in the context of the EPR–Bohm and the EPR–Bell experiments on a pair of spin 1/2 particles in the singlet state. It is argued that EPR's definition of e.p.r. is appropriate to the EPR–Bell experiment rather than to the EPR–Bohm experiment, and that Bohr's interpretation of e.p.r. is also consistent with such a viewpoint. It is shown that the observed correlation between the spins of the two particles in the EPR–Bell experiment is just a manifestation of the correlation that exists between the wave functions of the particles in the singlet state and a consequence of the fact that a Stern–Gerlach magnet does not change the state of a particle but only transforms its wave function into a representation defined by the axis of the magnet. As such, the correlation is suggested to be an affirmation of Einstein's concept of locality, and not an evidence for nonlocality.

scholarly journals Fast-forward of adiabatic dynamics in quantum mechanics

2009 ◽  
Vol 466 (2116) ◽  
pp. 1135-1154 ◽  
Author(s):  
Shumpei Masuda ◽  
Katsuhiro Nakamura
Keyword(s):  
Quantum Mechanics ◽  
Wave Functions ◽  
Final Time ◽  
Final State ◽  
Previous Theory ◽  
Adiabatic Dynamics ◽  
Short Time ◽  
Driving Potential ◽  
Adiabatic State ◽  
The Ideal

We propose a method to accelerate adiabatic dynamics of wave functions (WFs) in quantum mechanics to obtain a final adiabatic state except for the spatially uniform phase in any desired short time. In our previous work, acceleration of the dynamics of WFs was shown to obtain the final state in any short time by applying driving potential. We develop the previous theory of fast-forward to derive a driving potential for the fast-forward of adiabatic dynamics. A typical example is the fast-forward of adiabatic transport of a WF, which is the ideal transport in the sense that a stationary WF is transported to an aimed position in any desired short time without leaving any disturbance at the final time of the fast-forward. As other important examples, we show accelerated manipulations of WFs, such as their splitting and squeezing. The theory is also applicable to macroscopic quantum mechanics described by the nonlinear Schrödinger equation.

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