scholarly journals A quantum algorithm for spin chemistry: a Bayesian exchange coupling parameter calculator with broken-symmetry wave functions

2021 ◽  
Author(s):  
Kenji Sugisaki ◽  
Kazuo Toyota ◽  
Kazunobu Sato ◽  
Daisuke Shiomi ◽  
Takeji Takui
Keyword(s):  
Wave Function ◽  
Exchange Coupling ◽  
Coupling Parameter ◽  
Quantum Algorithm ◽  
Wave Functions ◽  
Broken Symmetry ◽  
Spin States ◽  
Spin Chemistry ◽  
Heisenberg Exchange ◽  
Total Energies

A quantum algorithm “Bayesian exchange coupling parameter calculator with broken-symmetry wave function (BxB)” enables us to calculate Heisenberg exchange coupling parameter J without inspecting total energies of individual spin states, within 1 kcal mol−1 of energy tolerance.

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.

scholarly journals INTEGRAL TRANSFORM TECHNIQUE FOR MESON WAVE FUNCTIONS

1996 ◽  
Vol 11 (20) ◽  
pp. 1611-1626 ◽  
Author(s):  
A.P. BAKULEV ◽  
S.V. MIKHAILOV
Keyword(s):  
Wave Function ◽  
Sum Rules ◽  
Integral Transform ◽  
Wave Functions ◽  
Sum Rule ◽  
New Approach ◽  
Exactly Solvable ◽  
The Stability ◽  
The Masses ◽  
Integral Transform Technique

In a recent paper1 we have proposed a new approach for extracting the wave function of the π-meson φπ(x) and the masses and wave functions of its first resonances from the new QCD sum rules for nondiagonal correlators obtained in Ref. 2. Here, we test our approach using an exactly solvable toy model as illustration. We demonstrate the validity of the method and suggest a pure algebraic procedure for extracting the masses and wave functions relating to the case under investigation. We also explore the stability of the procedure under perturbations of the theoretical part of the sum rule. In application to the pion case, this results not only in the mass and wave function of the first resonance (π′), but also in the estimation of π″-mass.

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.

LONG RANGE FORCES BETWEEN HYDROGEN MOLECULES

1955 ◽  
Vol 33 (11) ◽  
pp. 668-678 ◽  
Author(s):  
F. R. Britton ◽  
D. T. W. Bean
Keyword(s):  
Wave Function ◽  
Long Range ◽  
Ground State ◽  
Close Agreement ◽  
Van Der Waals ◽  
Wave Functions ◽  
Numerical Factor ◽  
Hydrogen Molecules ◽  
Static Quadrupole

Long range forces between two hydrogen molecules are calculated by using methods developed by Massey and Buckingham. Several terms omitted by them and a corrected numerical factor greatly change results for the van der Waals energy but do not affect their results for the static quadrupole–quadrupole energy. By using seven approximate ground state H2 wave functions information is obtained regarding the dependence of the van der Waals energy on the choice of wave function. The value of this energy averaged over all orientations of the molecular axes is found to be approximately −11.0 R−6 atomic units, a result in close agreement with semiempirical values.

scholarly journals DISTRIBUTION OF MAXIMA OF THE ANTISYMMETRIZED WAVE FUNCTION FOR THE NUCLEONS OF A CLOSED-SHELL AND FOR THE NUCLEONS OF ALL CLOSED-SHELLS IN A NUCLEUS.

2020 ◽  
Vol 15 ◽  
pp. 57
Author(s):  
G. S. Anagnostatos
Keyword(s):  
Wave Function ◽  
Mathematical Problem ◽  
Closed Shell ◽  
Wave Functions ◽  
Pictorial Representation ◽  
One Dimensional ◽  
Regular Polyhedra ◽  
Closed Shell Nuclei ◽  
Simple Systems ◽  
Closed Shells

The significant features of exchange symmetry are displayed by simple systems such as two identical, spinless fermions in a one-dimensional well with infinite walls. The conclusion is that the maxima of probability of the antisymmetrized wave function of these two fermions lie at the same positions as if a repulsive force (of unknown nature) was applied between these two fermions. This conclusion is combined with the solution of a mathematical problem dealing with the equilibrium of identical repulsive particles (of one or two kinds) on one or more spheres like neutrons and protons on nuclear shells. Such particles are at equilibrium only for specific numbers of particles and, in addition, if these particles lie on the vertices of regular polyhedra or their derivative polyhedra. Finally, this result leads to a pictorial representation of the structure of all closed shell nuclei. This representation could be used as a laboratory for determining nuclear properties and corresponding wave functions.

Spinless relativistic particle in energy-dependent potential and normalization of the wave function

Open Physics ◽  
2014 ◽  
Vol 12 (6) ◽  
Author(s):  
Amar Benchikha ◽  
Lyazid Chetouani
Keyword(s):  
Wave Function ◽  
Spectral Decomposition ◽  
Relativistic Particle ◽  
Wave Functions ◽  
Integral Approach ◽  
Normalizing Constant ◽  
Klein Gordon ◽  
Dependent Potential ◽  
Energy Dependent ◽  
Coulomb Potentials

AbstractThe problem of normalization related to a Klein-Gordon particle subjected to vector plus scalar energy-dependent potentials is clarified in the context of the path integral approach. In addition the correction relating to the normalizing constant of wave functions is exactly determined. As examples, the energy dependent linear and Coulomb potentials are considered. The wave functions obtained via spectral decomposition, were found exactly normalized.

scholarly journals IS IT POSSIBLE TO CONSTRUCT THE PROTON STRUCTURE FUNCTION BY LORENTZ-BOOSTING THE STATIC QUARK-MODEL WAVE FUNCTION?

2004 ◽  
Vol 19 (31) ◽  
pp. 5435-5442 ◽  
Author(s):  
Y. S. KIM ◽  
MARILYN E. NOZ
Keyword(s):  
Wave Function ◽  
Harmonic Oscillator ◽  
Structure Function ◽  
Parton Distribution ◽  
Wave Functions ◽  
Proton Structure Function ◽  
Proton Structure ◽  
Static Quark ◽  
Momentum Relation ◽  
Good Agreement

The energy-momentum relations for massive and massless particles are E=p2/2m and E=pc respectively. According to Einstein, these two different expressions come from the same formula [Formula: see text]. Quarks and partons are believed to be the same particles, but they have quite different properties. Are they two different manifestations of the same covariant entity as in the case of Einstein's energy-momentum relation? The answer to this question is YES. It is possible to construct harmonic oscillator wave functions which can be Lorentz-boosted. They describe quarks bound together inside hadrons. When they are boosted to an infinite-momentum frame, these wave functions exhibit all the peculiar properties of Feynman's parton picture. This formalism leads to a parton distribution corresponding to the valence quarks, with a good agreement with the experimentally observed distribution.

Integral equations and relations for Lamé functions and ellipsoidal wave functions

1968 ◽  
Vol 64 (1) ◽  
pp. 113-126 ◽  
Author(s):  
B. D. Sleeman
Keyword(s):  
Wave Function ◽  
Green’S Function ◽  
Integral Equations ◽  
Green's Function ◽  
Function Theory ◽  
Natural Generalization ◽  
Wave Functions ◽  
Linear Integral ◽  
First Time ◽  
Linear Integral Equations

AbstractNon-linear integral equations and relations, whose nuclei in all cases is the ‘potential’ Green's function, satisfied by Lamé polynomials and Lamé functions of the second kind are discussed. For these functions certain techniques of analysis are described and these find their natural generalization in ellipsoidal wave-function theory. Here similar integral equations are constructed for ellipsoidal wave functions of the first and third kinds, the nucleus in each case now being the ‘free space’ Green's function. The presence of ellipsoidal wave functions of the second kind is noted for the first time. Certain possible generalizations of the techniques and ideas involved in this paper are also discussed.

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.

Sign in / Sign up

Export Citation Format

Share Document