Calculation of a power spectrum and definition of wave functions of an ion Cr3+ in antiferromagnetic crystal Cr2O3 in the model of a crystalline field

2002 ◽  
Vol 88 (5) ◽  
pp. 676-680 ◽  
Author(s):  
I. S. Nikiforov ◽  
D. A. Filippov
Keyword(s):  
Power Spectrum ◽  
Wave Functions ◽  
Crystalline Field ◽  
Definition Of

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.

Calculation of Wave Functions in a Symmetrical Crystalline Field

1954 ◽  
Vol 95 (6) ◽  
pp. 1443-1449 ◽  
Author(s):  
Paul H. E. Meijer
Keyword(s):  
Wave Functions ◽  
Crystalline Field

Crystalline-field effect on ground-state wave functions of Cu2+ ions

1977 ◽  
Vol 42 (1) ◽  
pp. 77-84 ◽  
Author(s):  
B. N. Misra ◽  
Faujdar ◽  
R. Kripal
Keyword(s):  
Ground State ◽  
Field Effect ◽  
Wave Functions ◽  
Crystalline Field ◽  
State Wave

XI.—Reciprocity. Part III: Reciprocal Wave Functions

1940 ◽  
Vol 60 (2) ◽  
pp. 141-146 ◽  
Author(s):  
Max Born ◽  
Klaus Fuchs
Keyword(s):  
Fourier Coefficient ◽  
Scalar Product ◽  
Transcendental Equation ◽  
Wave Functions ◽  
Definition Of ◽  
Made In

The attempt to find reciprocal wave functions made in Part II led to some difficulties. We believe that these were due to an incorrect definition of the relativistic scalar product and Fourier coefficient. We shall show in this paper that a modification of these definitions leads to simpler equations, which allow us to determine the reciprocal wave functions and to find a transcendental equation for μ = aε/k, as was envisaged in Part I.

scholarly journals q-Schrödinger Equations for V = u2 + 1/u2 and Morse Potentials in Terms of the q-Canonical Transformation

1997 ◽  
Vol 12 (13) ◽  
pp. 2373-2384 ◽  
Author(s):  
Ö. F. Dayi ◽  
I. H. Duru
Keyword(s):  
Schrödinger Equation ◽  
Canonical Transformation ◽  
Schrodinger Equation ◽  
Laguerre Polynomials ◽  
Dynamical Symmetry ◽  
Wave Functions ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Definition Of ◽  
Morse Potentials

The realizations of the Lie algebra corresponding to the dynamical symmetry group SO(2,1) of the Schrödinger equations for the Morse and the V = u2 + 1/u2 potentials were known to be related by a canonical transformation. q-deformed analog of this transformation connecting two different realizations of the sl q(2) algebra is presented. By the virtue of the q-canonical transformation, a q-deformed Schrödinger equation for the Morse potential is obtained from the q-deformed V = u2 + 1/u2 Schrödinger equation. Wave functions and eigenvalues of the q-Schrödinger equations yielding a new definition of the q-Laguerre polynomials are studied.

scholarly journals THE GRAPH-REPRESENTATION APPROACH TO TOPOLOGICAL FIELD THEORY IN 2 + 1 DIMENSIONS

1992 ◽  
Vol 07 (03) ◽  
pp. 563-589
Author(s):  
STEPHEN P. MARTIN
Keyword(s):  
Field Theory ◽  
Poisson Bracket ◽  
Wave Functions ◽  
Graph Representation ◽  
Commutator Algebra ◽  
Gauge Transformations ◽  
Topological Quantum ◽  
Topological Field ◽  
Definition Of ◽  
Theory Of Graphs

An alternative definition of topological quantum field theory in 2 + 1 dimensions is discussed. The fundamental objects in this approach are not gauge fields as in the usual approach, but nonlocal observables associated with graphs. The classical theory of graphs is defined by postulating a simple diagrammatic rule for computing the Poisson bracket of any two graphs. The theory is quantized by exhibiting a quantum deformation of the classical Poisson-bracket algebra, which is realized as a commutator algebra on a Hilbert space of states. The wave functions in this "graph representation" approach are functionals on an appropriate set of graphs. This is in contrast to the usual "connection representation" approach, in which the theory is defined in terms of a gauge field and the wave functions are functionals on the space of flat spatial connections modulo gauge transformations.

scholarly journals PREDICTING THE VARIANCE OF A MEASUREMENT WITH 1/f NOISE

2013 ◽  
Vol 12 (01) ◽  
pp. 1350006 ◽  
Author(s):  
BENJAMIN LENOIR
Keyword(s):  
Power Spectrum ◽  
Flicker Noise ◽  
Random Processes ◽  
Power Spectrum Density ◽  
Alternative Definition ◽  
Measurement Duration ◽  
Spectrum Density ◽  
Measurement Devices ◽  
Definition Of ◽  
Stationary Random Processes

Measurement devices always add noise to the signal of interest and it is necessary to evaluate the variance of the results. This article focuses on stationary random processes whose power spectrum density is a power law of frequency. For flicker noise, behaving as 1/f and which is present in many different phenomena, the usual way to compute the variance leads to infinite values. This article proposes an alternative definition of the variance which takes into account the fact that measurement devises need to be calibrated. This new variance, which depends on the calibration duration, the measurement duration and the duration between the calibration and the measurement, allows avoiding infinite values when computing the variance of a measurement.

scholarly journals Non-Oscillatory Power Spectrum From States of Low Energy in Kinetically Dominated Early Universes

2021 ◽  
Vol 8 ◽  
Author(s):  
Mercedes Martín-Benito ◽  
Rita B. Neves ◽  
Javier Olmedo
Keyword(s):  
Power Spectrum ◽  
Quantum Cosmology ◽  
Initial Conditions ◽  
Power Spectra ◽  
Low Energy ◽  
Loop Quantum Cosmology ◽  
Test Function ◽  
Vacuum States ◽  
Oscillatory Power ◽  
Definition Of

Recently, States of Low Energy (SLEs) have been proposed as viable vacuum states of primordial perturbations within Loop Quantum Cosmology (LQC). In this work we investigate the effect of the high curvature region of LQC on the definition of SLEs. Shifting the support of the test function that defines them away from this regime results in primordial power spectra of perturbations closer to those of the so-called Non-oscillatory (NO) vacuum, which is another viable choice of initial conditions previously introduced in the LQC context. Furthermore, through a comparison with the Hadamard-like SLEs, we prove that the NO vacuum is of Hadamard type as well.

Quantum system: Wave function, entanglement and the uncertainty principle

2021 ◽  
pp. 2150222 ◽  
Author(s):  
A. V. Melkikh
Keyword(s):  
Wave Function ◽  
Quantum System ◽  
Uncertainty Principle ◽  
Wave Functions ◽  
Identical Particles ◽  
Quantum Particles ◽  
System Of Particles ◽  
Definition Of

A definition of entanglement based on the overlap of wave functions of identical particles is proposed. A definition of a quantum system of particles related to their entanglement with each other and the environment is proposed. It is shown that in the general case, the uncertainty principle cannot be formulated for a system of quantum particles in the form of a single inequality.

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