scholarly journals Symmetry, Transactions, and the Mechanism of Wave Function Collapse

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1373
Author(s):  
John Gleason Cramer ◽  
Carver Andress Mead
Keyword(s):  
Wave Function ◽  
Hydrogen Atom ◽  
Dimensional Space ◽  
Electromagnetic Coupling ◽  
Wave Functions ◽  
Single Electron ◽  
Matched Pair ◽  
Wave Mechanics ◽  
Conservation Of Energy ◽  
Wave Function Collapse

The Transactional Interpretation of quantum mechanics exploits the intrinsic time-symmetry of wave mechanics to interpret the ψ and ψ* wave functions present in all wave mechanics calculations as representing retarded and advanced waves moving in opposite time directions that form a quantum “handshake” or transaction. This handshake is a 4D standing-wave that builds up across space-time to transfer the conserved quantities of energy, momentum, and angular momentum in an interaction. Here, we derive a two-atom quantum formalism describing a transaction. We show that the bi-directional electromagnetic coupling between atoms can be factored into a matched pair of vector potential Green’s functions: one retarded and one advanced, and that this combination uniquely enforces the conservation of energy in a transaction. Thus factored, the single-electron wave functions of electromagnetically-coupled atoms can be analyzed using Schrödinger’s original wave mechanics. The technique generalizes to any number of electromagnetically coupled single-electron states—no higher-dimensional space is needed. Using this technique, we show a worked example of the transfer of energy from a hydrogen atom in an excited state to a nearby hydrogen atom in its ground state. It is seen that the initial exchange creates a dynamically unstable situation that avalanches to the completed transaction, demonstrating that wave function collapse, considered mysterious in the literature, can be implemented with solutions of Schrödinger’s original wave mechanics, coupled by this unique combination of retarded/advanced vector potentials, without the introduction of any additional mechanism or formalism. We also analyze a simplified version of the photon-splitting and Freedman–Clauser three-electron experiments and show that their results can be predicted by this formalism.

The Wave Theory of the Electron

1928 ◽  
Vol 24 (4) ◽  
pp. 501-505 ◽  
Author(s):  
J. M. Whittaker
Keyword(s):  
Wave Function ◽  
Differential Equations ◽  
Fourth Order ◽  
Commutative Algebra ◽  
Wave Theory ◽  
Wave Functions ◽  
Linear Differential Equations ◽  
Wave Mechanics ◽  
First Order ◽  
Linear Differential

In two recent papers Dirac has shown how the “duplexity” phenomena of the atom can be accounted for without recourse to the hypothesis of the spinning electron. The investigation is carried out by the methods of non-commutative algebra, the wave function ψ being a matrix of the fourth order. An alternative presentation of the theory, using the methods of wave mechanics, has been given by Darwin. The four-rowed matrix ψ is replaced by four wave functions ψ1, ψ2, ψ3, ψ4 satisfying four linear differential equations of the first order. These functions are related to one particular direction, and the work can only be given invariance of form at the expense of much additional complication, the four wave functions being replaced by sixteen.

ENERGY-DEPENDENT POTENTIAL AND NORMALIZATION OF WAVE FUNCTION

2013 ◽  
Vol 28 (18) ◽  
pp. 1350079 ◽  
Author(s):  
A. BENCHIKHA ◽  
L. CHETOUANI
Keyword(s):  
Wave Function ◽  
Hydrogen Atom ◽  
Harmonic Oscillator ◽  
Path Integral ◽  
Spectral Decomposition ◽  
Wave Functions ◽  
Integral Approach ◽  
Path Integral Approach ◽  
Dependent Potential ◽  
Energy Dependent

The problem of normalization related to energy-dependent potentials is examined in the context of the path integral approach, and a justification is given. As examples, the harmonic oscillator and the hydrogen atom (radial) where, respectively the frequency and the Coulomb's constant depend on energy, are considered and their propagators determined. From their spectral decomposition, we have found that the wave functions extracted are correctly normalized.

Wave Mechanics

2019 ◽  
pp. 91-174
Author(s):  
P.J.E. Peebles
Keyword(s):  
Magnetic Field ◽  
Wave Function ◽  
Angular Momentum ◽  
Hydrogen Atom ◽  
Physical System ◽  
Adjoint Operator ◽  
Physical Application ◽  
Wave Mechanics ◽  
Definite Form ◽  
Quantum Wave

This chapter develops the wave mechanics formalism. The emphasis here is on symmetries and conservation laws: parity, linear and angular momentum, and the electromagnetic interaction. The only specific physical application is the completion of the study of an isolated hydrogen atom, with some discussion of the motion of a particle in a magnetic field. The chapter also outlines the general assumptions of quantum wave mechanics, which may be summarized as follows: the state of a physical system is represented by a wave function and each measurable attribute of the system is represented by a linear self-adjoint operator in the space of functions. To apply these general assumptions to a given physical system, one must give a specific prescription for the observables and their algebra, and one must adopt a definite form for the Hamiltonians as a function of the observables.

On the theory of elastic collisions between electrons and hydrogen atoms

1960 ◽  
Vol 254 (1277) ◽  
pp. 259-272 ◽  
Keyword(s):  
Wave Function ◽  
Hydrogen Atom ◽  
Boundary Conditions ◽  
Continuous Spectrum ◽  
Ground State ◽  
Wave Functions ◽  
Hydrogen Atoms ◽  
Complete Set ◽  
Exchange Scattering ◽  
Conditions At Infinity

A hydrogen atom in the ground state scatters an electron with kinetic energy too small for inelastic collisions to occur. The wave function Ψ(r 1 ; r 2 ) of the system has boundary conditions at infinity which must be chosen to allow correctly for the possibilities of both direct and exchange scattering. The expansion Ψ = Σ ψ,(r 1 )F y (r 2 ) of the total wave function in y terms of a complete set of hydrogen atom wave functions ψ y (r 1 ) includes an integration over the continuous spectrum. It is si own that the integrand contains a singularity. The explicit form of this singularity and its connexion with the boundary conditions are examined in detail. The symmetrized functions Y* may be represented by expansions of the form Σ {ψ y (r 1 ) G y ±(r 2 ) ±ψ y (r 2 ) y G y ±(r 1 )}, where the integrand in the continuous spectrum does not involve singularities. Finally, it is shown that because all the states ψ y of the hydrogen atom are included in the expansion, the equation satisfied by F 1 , the coefficient of the ground state, contains a polarization potential which behaves like — a/2 r 4 for large r and is independent of the velocity of the incident electron.

scholarly journals A LAGUERRE POLYNOMIAL ORTHOGONALITY AND THE HYDROGEN ATOM

2003 ◽  
Vol 01 (02) ◽  
pp. 177-188 ◽  
Author(s):  
CHARLES F. DUNKL
Keyword(s):  
Wave Function ◽  
Hydrogen Atom ◽  
Coulomb Potential ◽  
Elementary Proof ◽  
Laguerre Polynomial ◽  
Energy Levels ◽  
Laguerre Polynomials ◽  
Wave Functions ◽  
Radial Part ◽  
Meixner Polynomials

The radial part of the wave function of an electron in a Coulomb potential is the product of a Laguerre polynomial and an exponential with the variable scaled by a factor depending on the degree. This note presents an elementary proof of the orthogonality of wave functions with differing energy levels. It is also shown that this is the only other natural orthogonality for Laguerre polynomials. By expanding in terms of the usual Laguerre polynomial basis, an analogous strange orthogonality is obtained for Meixner polynomials.

Lower-bound energies and the Virial theorem in wave mechanics

1961 ◽  
Vol 57 (2) ◽  
pp. 341-347 ◽  
Author(s):  
G. L. Caldow ◽  
C. A. Coulson
Keyword(s):  
Wave Function ◽  
Lower Bound ◽  
Variational Method ◽  
Harmonic Oscillator ◽  
Lower Bounds ◽  
Ground State ◽  
Virial Theorem ◽  
Wave Functions ◽  
Wave Mechanics ◽  
Mechanical Problem

ABSTRACTSeveral forms of the lower-bound variational method for the calculation of the eigenvalues in a wave-mechanical problem are considered, and compared; the particular case of the harmonic oscillator being chosen. All forms have certain unsatisfactory features, but some of them are considerably worse than others. One reason why calculations of lower bounds are in general less satisfactory than Ritz-type calculations of an upper bound is shown to be that whereas, in the presence of a scale factor, this latter wave-function satisfies the virial theorem, in none of the lower-bound wave-functions is this true. Similar calculations are reported for the ground state of the helium atom.

scholarly journals Visualization of Schrodinger Equations Polar Wave Functions for Non-Central Coulombic Rosen Morse Potential in ExcitationState nr = 2 and l = 1

2019 ◽  
Vol 2 ◽  
pp. 173-176
Author(s):  
Cecilia Yanuarief
Keyword(s):  
Wave Function ◽  
Hydrogen Atom ◽  
Morse Potential ◽  
Function Analysis ◽  
The State ◽  
Wave Functions ◽  
Polynomial Method ◽  
Polar Function ◽  
Potential System ◽  
Polar Wave

Research has been conducted which shows the quantization visualization of hydrogen atom orbitals angular space in Rosen Morse potential system interference when the electrons are excited in the state of  nr= 2 and l = 1 through the polar function analysis of the Schrödinger Potential of Non-Central Coloumbic Rosen Morse. The polar Schrödinger equation is solved using the Romanovski polynomial method to obtain the polar wave function. To show the accuracy of the analysis, the polar wave function spectrum i s visualized with Matlab-based computer programming.

Note on Pauli's Exclusion Principle

1928 ◽  
Vol 24 (3) ◽  
pp. 445-446 ◽  
Author(s):  
H. D. Ursell
Keyword(s):  
Wave Function ◽  
Wave Functions ◽  
Exclusion Principle ◽  
Simple Explanation ◽  
Wave Mechanics ◽  
Image Position

A simple explanation of Pauli's principle was first given with the wave mechanics. Its interpretation in the new theory was that the wave functions of Schrödinger were antisymmetrical in all the electrons concerned. Thus when the interactions of the electrons may be neglected, the wave function (for a system of n electrons) can never be of the formin nature, but only of the formHence σ, τ,…ω must be all distinct.

Gravity as the curvature of the wave function of the universe.

2019 ◽  
Author(s):  
Vitaly Kuyukov
Keyword(s):  
Wave Function ◽  
Wave Functions ◽  
Main Task ◽  
Reference Systems ◽  
Theory Of Relativity ◽  
General Theory Of Relativity ◽  
Principle Of Equivalence ◽  
Relative Wave Function ◽  
New Equation ◽  
The Universe

Modern general theory of relativity considers gravity as the curvature of space-time. The theory is based on the principle of equivalence. All bodies fall with the same acceleration in the gravitational field, which is equivalent to locally accelerated reference systems. In this article, we will affirm the concept of gravity as the curvature of the relative wave function of the Universe. That is, a change in the phase of the universal wave function of the Universe near a massive body leads to a change in all other wave functions of bodies. The main task is to find the form of the relative wave function of the Universe, as well as a new equation of gravity for connecting the curvature of the wave function and the density of matter.

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