Monopole and quadrupole incompressibility of the hydrogen atom using deformed oscillation trial wave functions

1995 ◽  
pp. 309-311
Author(s):  
L. Zamick
Keyword(s):  
Hydrogen Atom ◽  
Wave Functions

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.

Wave functions for the hydrogen atom in a dense plasma

2003 ◽  
Vol 81 (11) ◽  
pp. 1243-1248 ◽  
Author(s):  
Y P Varshni
Keyword(s):  
Hydrogen Atom ◽  
Dense Plasma ◽  
Wave Functions ◽  
Electron Interaction ◽  
Dipole Polarizability ◽  
Variational Wave Functions ◽  
Absorption Oscillator Strength ◽  
Variational Wave ◽  
Good Agreement ◽  
03.65 Ge

A hydrogen atom in a high-density plasma is simulated by a model in which the hydrogen atom is confined in an impenetrable spherical box, with the atom at the centre. For the proton–electron interaction the Debye–Huckel potential is used. Variational wave functions are proposed for the 1s and 2p states. Energies calculated from these for different values of the radius of box (r0) are shown to be in good agreement with the exact values. The variational wave functions are further employed to calculate the absorption oscillator strength for the 1s [Formula: see text] 2p transition and the dipole polarizability for different values of r0. PACS Nos.: 03.65.Ge, 32.70.Os, 31.70.Dk, 52.20.–j

Explicit spheroidal wave functions of the hydrogen atom

2011 ◽  
Vol 63 (1) ◽  
pp. 81-87 ◽  
Author(s):  
T. Kereselidze ◽  
Z. S. Machavariani ◽  
G. Chkadua
Keyword(s):  
Hydrogen Atom ◽  
Wave Functions ◽  
Spheroidal Wave Functions

The use of Gaussian (exponential quadratic) wave functions in molecular problems. II. Wave functions for the ground states of the hydrogen atom and of the hydrogen molecule

1960 ◽  
Vol 258 (1294) ◽  
pp. 421-430 ◽  
Keyword(s):  
Hydrogen Atom ◽  
Quadratic Form ◽  
Hydrogen Molecule ◽  
Ground States ◽  
Cylindrical Symmetry ◽  
Binding Energies ◽  
Wave Functions ◽  
Electronic Wave ◽  
Electronic Wave Functions ◽  
Independent Parameters

The results reported in this paper constitute a first examination of the use of Gaussian wave functions with correlation as approximations to electronic wave functions. Functions of the form Σ k = n k =1 C k exp ( – Q k ), where C k is a constant and Q k is a quadratic form corresponding to orbitals with cylindrical symmetry, variable centres and with correlation, are used for the hydrogen molecule. Binding energies of 4∙30, 4∙42, 4∙52 and 4∙58 eV are obtained with functions containing, respectively, 26, 35, 53 and 71 independent parameters. The accuracy of the results and the moderate computing times suggest that there is considerable scope for wave functions of this type. For the hydrogen atom, approximations to the 1 s -orbital in terms of Σ k = n k =1 C k exp ( – a k r 2 ) are given for n = 3, 4, 5, 6 and 8.

The partial wave theory of electron-hydrogen atom collisions

1957 ◽  
Vol 53 (3) ◽  
pp. 654-662 ◽  
Author(s):  
I. C. Percival ◽  
M. J. Seaton
Keyword(s):  
Hydrogen Atom ◽  
Partial Wave ◽  
Cross Sections ◽  
Wave Theory ◽  
Wave Functions ◽  
Scattered Electron ◽  
Hartree Fock ◽  
Angular Momenta ◽  
Continuous State ◽  
Approximate Wave

ABSTRACTThe paper is concerned with the solution of the algebraic problems arising in the partial wave treatment of electron-hydrogen atom collisions. Explicitly antisymmetrized wave functions are used throughout. The boundary conditions are written in S-matrix notation and expressions for total and differential cross-sections obtained. The algebraic coefficients fλ and gλ occurring in the continuous state Hartree-Fock equations are expressed in terms of Racah coefficients, and tabulated as functions of the total angular momentum for atomic s, p and d electrons and all angular momenta of the scattered electron. Expressions are given for the calculation of first-order corrections to the results obtained using approximate wave functions.

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.

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