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.

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.

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.

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.

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.

Operators and meaning of wave function

2016 ◽  
pp. 4039-4042
Author(s):  
Viliam Malcher
Keyword(s):  
Wave Function ◽  
Quantum Theory ◽  
State Vector ◽  
The State ◽  
Physical Significance ◽  
Central Problem ◽  
Quantum Mechanical ◽  
Mechanical Description ◽  
Quantum Mechanical Description ◽  
Interpretation Of Quantum Theory

The interpretation problems of quantum theory are considered. In the formalism of quantum theory the possible states of a system are described by a state vector. The state vector, which will be represented as |ψ> in Dirac notation, is the most general form of the quantum mechanical description. The central problem of the interpretation of quantum theory is to explain the physical significance of the |ψ>. In this paper we have shown that one of the best way to make of interpretation of wave function is to take the wave function as an operator.

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.

The Right to Education in India

2019 ◽  
Author(s):  
Florian Matthey-Prakash
Keyword(s):  
Private Education ◽  
The State ◽  
Legal Empowerment ◽  
Right To Education ◽  
The Poor ◽  
Potential System ◽  
Education In India ◽  
Alternative Means ◽  
Education Act ◽  
The Right

What does it mean for education to be a fundamental right, and how may children benefit from it? Surprisingly, even when the right to education was added to the Indian Constitution as Article 21A, this question received barely any attention. This book identifies justiciability (or, more broadly, enforceability) as the most important feature of Article 21A, meaning that children and their parents must be provided with means to effectively claim their right from the state. Otherwise, it would remain a ‘right’ only on paper. The book highlights how lack of access to the Indian judiciary means that the constitutional promise of justiciability is unfulfilled, particularly so because the poor, who cannot afford quality private education for their children, must be the main beneficiaries of the right. It then deals with possible alternative means the state may provide for the poor to claim the benefits under Article 21A, and identifies the grievance redress mechanism created by the Right to Education Act as a potential system of enforcement. Even though this system is found to be deficient, the book concludes with an optimistic outlook, hoping that rights advocates may, in the future, focus on improving such mechanisms for legal empowerment.

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