Numerical method for the propagation of quantum-mechanical wave functions in phase space

1991 ◽  
Vol 67 (19) ◽  
pp. 2601-2604 ◽  
Author(s):  
Go. Torres-Vega ◽  
John H. Frederick
Keyword(s):  
Phase Space ◽  
Numerical Method ◽  
Wave Functions ◽  
Quantum Mechanical ◽  
Mechanical Wave

NEW n-MODE BOSE OPERATOR REALIZATION OF SU(2) LIE ALGEBRA AND ITS APPLICATION IN ENTANGLED FRACTIONAL FOURIER TRANSFORM

2009 ◽  
Vol 24 (08) ◽  
pp. 615-624 ◽  
Author(s):  
HONG-YI FAN ◽  
SHU-GUANG LIU
Keyword(s):  
Fourier Transform ◽  
Lie Algebra ◽  
Fractional Fourier Transform ◽  
Wave Functions ◽  
Entangled State ◽  
Quantum Mechanical ◽  
Mechanical Wave ◽  
Bose Operator ◽  
Operator Realization ◽  
Multipartite Entangled State

We introduce a new n-mode Bose operator realization of SU(2) Lie algebra and link it to the two mutually conjugate multipartite entangled state representations. In so doing we are naturally lead to the n-mode entangle fractional Fourier transform (EFFT), which provides us with a convenient way to deriving the EFFT of quantum-mechanical wave functions.

Numbers and Shapes

2020 ◽  
pp. 36-53
Author(s):  
Demetris Nicolaides
Keyword(s):  
Mathematical Analysis ◽  
Scientific Method ◽  
Wave Functions ◽  
Quantum Mechanical ◽  
The Sun ◽  
Mechanical Wave ◽  
The Earth ◽  
Copernican Revolution ◽  
Modern Physics ◽  
Theory Of Forms

Pythagoras initiated the mathematical analysis of nature, a cornerstone practice in modern physics. “Things are numbers” is the most significant Pythagorean doctrine. It signifies that the phenomena of nature are describable by equations and numbers. Therefore, nature is quantifiable and potentially knowable through the scientific method. The Pythagoreans quantified pleasing sounds of music, right-angled triangles, even the motion of the heavenly bodies. The “Copernican revolution” (heliocentricity) is traced back to Pythagorean cosmology. But, finally, Einstein’s relativity clarifies a popular misconception related to it: that “the earth revolves around the sun (heliocentricity) is correct,” and that “the sun revolves around the earth (geocentricism) is incorrect.” Plato was inspired by Pythagorean mathematics, but he replaced “things are numbers” with things are shapes, forms, Forms, a noetic description of nature known as the theory of “Forms.” The quantum-mechanical wave-functions—mathematical forms that describe microscopic particles—are the Platonic Forms of quarks and leptons.

Stationary properties of approximate wave functions

1969 ◽  
Vol 47 (21) ◽  
pp. 2355-2361 ◽  
Author(s):  
A. R. Ruffa
Keyword(s):  
Wave Function ◽  
Total Energy ◽  
Helium Atom ◽  
Wave Functions ◽  
Quantum Mechanical ◽  
Mechanical Wave ◽  
Expectation Value ◽  
Charge Densities ◽  
Hartree Fock ◽  
Approximate Wave

The accuracy of quantum mechanical wave functions is examined in terms of certain stationary properties. The most elementary of these, namely that displayed by the class of wave functions which yields a stationary value for the total energy of the system, is demonstrated to necessarily require few other stationary properties, and none of these appear to be particularly useful. However, the class of wave functions which yields both stationary energies and charge densities has very important stationary properties. A theorem is proven which states that any wave function in this class yields a stationary expectation value for any operator which can be expressed as a sum of one-particle operators. Since the Hartree–Fock wave function is known to possess these same stationary properties, this theorem demonstrates that the Hartree–Fock wave function is one of the infinitely many wave functions of the class. Methods for generating other wave functions in this class by modifying the Hartree–Fock wave function without changing its stationary properties are applied to the calculation of wave functions for the helium atom.

scholarly journals On the Quantum Mechanical Wave Function as a Link Between Cognition and the Physical World: A Role for Psychology

2020 ◽  
Author(s):  
Douglas Michael Snyder
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Physical World ◽  
Wave Functions ◽  
Human Cognition ◽  
Quantum Mechanical ◽  
Mechanical Wave ◽  
Empirical Level ◽  
And Behavior ◽  
Empirical Demonstration

A straightforward explanation of fundamental tenets of quantum mechanics concerning the wave function results in the thesis that the quantum mechanical wave function is a link between human cognition and the physical world. The reticence on the part of physicists to adopt this thesis is discussed. A comparison is made to the behaviorists’ consideration of mind, and the historical roots of how the problem concerning the quantum mechanical wave function arose are discussed. The basis for an empirical demonstration that the wave function is a link between human cognition and the physical world is provided through developing an experiment using methodology from psychology and physics. Based on research in psychology and physics that relied on this methodology, it is likely that Einstein, Podolsky, and Rosen’s theoretical result that mutually exclusive wave functions can simultaneously apply to the same concrete physical circumstances can be implemented on an empirical level. Original article in The Journal of Mind and Behavior is on JSTOR at https://www.jstor.org/stable/pdf/43853678.pdf?seq=1 . Preprint on CERN preprint server at https://cds.cern.ch/record/569426 .

scholarly journals On Whether People Have the Capacity to Make Observations of Mutually Exclusive Physical Phenomena

2021 ◽  
Author(s):  
Douglas Michael Snyder
Keyword(s):  
Wave Function ◽  
Sigmund Freud ◽  
Physical System ◽  
William James ◽  
Wave Functions ◽  
Quantum Mechanical ◽  
Human Observer ◽  
Physical Interaction ◽  
Mechanical Wave ◽  
Physical Phenomena

It has been shown by Einstein, Podolsky, and Rosen that in quantum mechanics one of two different wave functions predicting specific values for quantities represented by non-commuting Hermitian operators can characterize the same physical system, without a physical interaction responsible for which wave function is realized in a measurement. This result means that one can make predictions regarding mutually exclusive features of a physical system. It is important to ask whether people can make observations of mutually exclusive phenomena. Our everyday experience informs us that a human observer is capable of observing one set of physical circumstances at a time. Evidence from psychology, though, indicates that people may have the capacity to make observations of mutually exclusive physical phenomena, even though this capacity in not generally recognized. Working independently, Sigmund Freud and William James provided some of this evidence. How the nature of the quantum mechanical wave function is associated with the problem posed by Einstein, Podolsky, and Rosen is addressed at the end of the paper.

scholarly journals And Where are Fluctuations In Quantum-Mechanical Wave Function?

2020 ◽  
Vol 1 (1) ◽  
Keyword(s):  
Wave Functions ◽  
Quantum Mechanical ◽  
Complex Numbers ◽  
Potential Well ◽  
Bohr Radius ◽  
Mechanical Wave ◽  
Generalized Complex ◽  
Different Types ◽  
Generalized Complex Numbers ◽  
Weight Coefficients

The generalized complex numbers containing weight coefficients for a paraxial case are described. An evident analogy between the wavy systems of trajectories, the module and an argument of complex numbers and the module and an argument of wave functions is drawn.Their geometrical interpretation is given on the plane and on the sphere. The symmetric and asymmetrical systems of wavy trajectories are considered. The examination of different types of wavy and zigzag trajectories of our systems of rays is presented. An evident analogy of these systems and wave functions describing finding of an electron in a potential well and near an atomic nucleus is drawn. The possible arrangement of a wave of de Broglie of an electron on the sphere of Bohr radius is shown. In the offered work great mathematicians whose works are connected with researches of complex numbers are marked out in {braces}: {Cardano, Hamilton, Gauss, Cauchy and Euler}.

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