scholarly journals Quantum Theory of Massless Particles in Stationary Axially Symmetric Spacetimes

Entropy ◽  
2021 ◽  
Vol 23 (9) ◽  
pp. 1205
Author(s):  
Amnon Moalem ◽  
Alexander Gersten
Keyword(s):  
Wave Function ◽  
Minkowski Spacetime ◽  
Wave Functions ◽  
Axially Symmetric ◽  
Principle Of Equivalence ◽  
Massless Particles ◽  
Radial Wave ◽  
Symmetric Spacetimes ◽  
Quantum Equations ◽  
Normalization Function

Quantum equations for massless particles of any spin are considered in stationary uncharged axially symmetric spacetimes. It is demonstrated that up to a normalization function, the angular wave function does not depend on the metric and practically is the same as in the Minkowskian case. The radial wave functions satisfy second order nonhomogeneous differential equations with three nonhomogeneous terms, which depend in a unique way on time and space curvatures. In agreement with the principle of equivalence, these terms vanish locally, and the radial equations reduce to the same homogeneous equations as in Minkowski spacetime.

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.

ON ASYMPTOTICS OF THREE-BODY BOUND STATE RADIAL WAVE FUNCTIONS OF HALO NUCLEI NEAR THE HYPERANGLE φ~0 AND φ~π/2 IN THE CONFIGURATION SPACE AND THREE-BODY ASYMPTOTIC NORMALIZATION FACTORS FOR 6He NUCLEUS IN THE (n+n+α)-CHANNEL

2009 ◽  
Vol 18 (07) ◽  
pp. 1561-1585 ◽  
Author(s):  
R. YARMUKHAMEDOV ◽  
M. K. UBAYDULLAEVA
Keyword(s):  
Wave Function ◽  
Configuration Space ◽  
Bound State ◽  
Wave Functions ◽  
Halo Nuclei ◽  
Asymptotic Normalization ◽  
Radial Wave ◽  
Asymptotic Expressions ◽  
Three Body ◽  
Normalization Factors

Asymptotic expressions for the bound state radial partial wave functions of three-body (nnc) halo nuclei with two loosely bound valence neutrons (n) are obtained in explicit form, when the relative distance between two neutrons (r) tends to infinity and the relative distance between the center of mass of core (c) and two neutrons (ρ) is too small or vice versa. These asymptotic expressions contain a factor that can strongly influence the asymptotic values of the three-body radial wave function in the vicinity of the hyperangle of φ~0 except 0 (r→∞ and ρ is too small except 0) or φ~π/2 except π/2 (ρ→∞ and r is too small except 0) in the configuration space. The derived asymptotic forms are applied to the analysis of the asymptotic behavior of the three-body (nnα) wave function for 6He nucleus obtained by other authors on the basis of multicluster stochastic variational method using the two forms of the αN-potential. The ranges of r (or ρ) from the asymptotical regions are determined for which the agreement between the calculated wave function and the asymptotics formulae is reached. Information about the values of the three-body asymptotic normalization factors is extracted.

Atomic wave functions for gold and thallium

1955 ◽  
Vol 51 (3) ◽  
pp. 486-503 ◽  
Author(s):  
A. S. Douglas ◽  
D. R. Hartree ◽  
W. A. Runciman
Keyword(s):  
Wave Function ◽  
Absorption Edge ◽  
Radial Wave Function ◽  
Wave Functions ◽  
Radial Wave ◽  
Consistent Field ◽  
Self Consistent ◽  
Self Consistent Field ◽  
Independent Variable ◽  
Independent Calculation

Before the war, self-consistent field calculations for the Au+ ion had been carried out by W. Hartree but were left still unpublished at his death (see prefatory note in (5)). These results have been used by Brenner and Brown (1) in a relativistic calculation of the K-absorption edge for gold, and they were also used in obtaining initial estimates for the partial self-consistent field calculations for thallium of which results are given in §§3–5 of the present paper. In the meantime an independent calculation for Au+ has been carried out by Henry (6), and his results agree closely with those of W. Hartree. However, it still seems desirable to publish the latter, since they give directly the radial wave function P(nl; r) at exact values of r, whereas Henry used log r as independent variable, as had been done for similar calculations for Hg(4), and has tabulated r½P(nl; r) which is the natural dependent variable to use with log r as independent variable (2); in some applications it is more convenient to have the radial wave functions themselves.

The interpolation of atomic wave functions

1955 ◽  
Vol 51 (4) ◽  
pp. 684-692 ◽  
Author(s):  
D. R. Hartree
Keyword(s):  
Wave Function ◽  
Atomic Number ◽  
Radial Wave Function ◽  
Point Of View ◽  
Wave Functions ◽  
Radial Wave ◽  
Atomic Wave ◽  
The Mean

ABSTRACTIf r̄nl is the mean radius for the radial wave function of a complete (nl) group in an atom of atomic number N, the variation of 1/r̄nl with N is nearly linear. Further the variation of a given (nl) radial wave function with N is such that for a given value of (r/r̄nl), the variation of the quantity (r̄nl)½P(nl; r) with r̄nl is nearly linear. These relations between the radial wave functions for different atoms are examined from the point of view of using them as a means of interpolating, with respect to atomic number, between results for atoms for which solutions of Fock's equations have been carried out.

The limiting behaviour of atomic wave functions for large atomic number

1957 ◽  
Vol 239 (1218) ◽  
pp. 311-319 ◽  
Keyword(s):  
Wave Function ◽  
Atomic Number ◽  
Radial Wave Function ◽  
Wave Functions ◽  
Radial Wave ◽  
Large Atomic Number ◽  
Limiting Behaviour ◽  
Set Up ◽  
Derivatives Of ◽  
Limiting Values

If P(nl; r) is the ( nl ) radial wave function in an atom of atomic number N , and P H ( nl; r ) is the corresponding wave function of hydrogen, then, for a given configuration and for large N N -1/2 P(nl; r) = P H (nl;Nr) +(1/ N ) Q(nl;Nr) + O (1/ N 2 ) The equations for the functions Q(nl; Nr) have been set up and solved for a number of ( nl ) values and configurations of up to twenty-eight electrons. From the solutions, the limiting values as N -> oo of certain screening numbers o( nl ) have been determined, so that estimation of o( nl ) for atoms of atomic number higher than any for which calculation of wave functions frag been carried out becomes a process of interpolation instead of extrapolation. It is found that for given configuration o( nl ) is nearly linear in the mean radius r over the whole range from N ->oo to the neutral atom. For a given value of r/r(nl) , r 1/2 P N (nl; r) is nearly linear in r. The r derivatives of this function at r = 0 can also be evaluated from the Q(nl; Nr) functions.

scholarly journals Cross sections for 2-to-1 meson–meson scattering

2021 ◽  
Vol 81 (3) ◽  
Author(s):  
Wan-Xia Li ◽  
Xiao-Ming Xu ◽  
H. J. Weber
Keyword(s):  
Wave Function ◽  
Relative Motion ◽  
Cross Sections ◽  
Heavy Ion ◽  
Wave Functions ◽  
Hadronic Matter ◽  
Radial Wave ◽  
Transition Potential ◽  
Transition Amplitudes ◽  
The Spectator

AbstractWe study the processes $$K{\bar{K}} \rightarrow \phi $$ K K ¯ → ϕ , $$\pi D \rightarrow D^*$$ π D → D ∗ , $$\pi {\bar{D}} \rightarrow {\bar{D}}^*$$ π D ¯ → D ¯ ∗ , and the production of $$\psi (3770)$$ ψ ( 3770 ) , $$\psi (4040)$$ ψ ( 4040 ) , $$\psi (4160)$$ ψ ( 4160 ) , and $$\psi (4415)$$ ψ ( 4415 ) mesons in collisions of charmed mesons or charmed strange mesons. The process of 2-to-1 meson–meson scattering involves a quark and an antiquark from the two initial mesons annihilating into a gluon and subsequently the gluon being absorbed by the spectator quark or antiquark. Transition amplitudes for the scattering process derive from the transition potential in conjunction with mesonic quark–antiquark wave functions and the relative-motion wave function of the two initial mesons. We derive these transition amplitudes in the partial wave expansion of the relative-motion wave function of the two initial mesons so that parity and total-angular-momentum conservation are maintained. We calculate flavor and spin matrix elements in accordance with the transition potential and unpolarized cross sections for the reactions using the transition amplitudes. Cross sections for the production of $$\psi (4040)$$ ψ ( 4040 ) , $$\psi (4160)$$ ψ ( 4160 ) , and $$\psi (4415)$$ ψ ( 4415 ) relate to nodes in their radial wave functions. We suggest the production of $$\psi (4040)$$ ψ ( 4040 ) , $$\psi (4160)$$ ψ ( 4160 ) , and $$\psi (4415)$$ ψ ( 4415 ) as probes of hadronic matter that results from the quark–gluon plasma created in ultrarelativistic heavy-ion collisions.

scholarly journals Quantum Cosmology with Third Quantisation

Universe ◽  
2021 ◽  
Vol 7 (11) ◽  
pp. 404
Author(s):  
Salvador J. Robles-Pérez
Keyword(s):  
Wave Function ◽  
Minkowski Spacetime ◽  
Wave Functions ◽  
Quantum Field ◽  
Isotropic Universe ◽  
Connected Manifold ◽  
The Third ◽  
Simply Connected ◽  
The Universe ◽  
Natural Way

We reviewed the canonical quantisation of the geometry of the spacetime in the cases of a simply and a non-simply connected manifold. In the former, we analysed the information contained in the solutions of the Wheeler–DeWitt equation and showed their interpretation in terms of the customary boundary conditions that are typically imposed on the semiclassical wave functions. In particular, we reviewed three different paradigms for the quantum creation of a homogeneous and isotropic universe. For the quantisation of a non-simply connected manifold, the best framework is the third quantisation formalism, in which the wave function of the universe is seen as a field that propagates in the space of Riemannian 3-geometries, which turns out to be isomorphic to a (part of a) 1+5 Minkowski spacetime. Thus, the quantisation of the wave function follows the customary formalism of a quantum field theory. A general review of the formalism is given, and the creation of the universes is analysed, including their initial expansion and the appearance of matter after inflation. These features are presented in more detail in the case of a homogeneous and isotropic universe. The main conclusion in both cases is that the most natural way in which the universes should be created is in entangled universe–antiuniverse pairs.

scholarly journals Calculated wave functions and energy values for X-ray terms of potassium

1939 ◽  
Vol 172 (949) ◽  
pp. 242-263 ◽  
Keyword(s):  
Wave Function ◽  
Radial Wave Function ◽  
Energy Parameter ◽  
Static Field ◽  
Wave Functions ◽  
Radial Wave ◽  
X Ray ◽  
Self Consistent Field ◽  
Approximate Wave ◽  
Made In

Calculations of approximate wave functions, carried out by the method of the self-consistent field (Hartree 1928), have now been made for a number of atoms and ions, and energy values of terms of the optical spectrum, based on these calculations, have been made in a few cases (for example, McDougall 1932). But, apart from the work considered in the present paper, the calculations for ions have all been for atoms ionized in the outermost group; no calculations of wave functions for atoms ionized in an inner group, and consequently no proper calculations of X-ray energies, have previously been made. It has been found empirically that the calculated value of the energy parameter e appearing in the equation for the radial wave function of an inner group is in very close agreement with the observed value of v / R for the corresponding X-ray term, but it is by no means clear why the agreement should be as close as it is, since the two quantities are really not directly comparable, as has already been pointed out (see, for example, Hartree 1928, pp. 116-17, 123 and Hartree 1933, pp. 288-90). The value of ϵ in the equation for the radial wave function P ( nl ) would be the energy required to remove an electron from that wave function if the rest of the atom were a static field of force, unaffected by the removal of that electron. Actually the atom is a configuration of electrons which changes when one of them, particularly an inner one, is removed. Further, the interaction energy of any one electron with the rest of the atom includes exchange terms as well as the direct Coulomb interaction which is all that is taken into account in considering any one electron as in the field of the rest of the atom regarded as a static field.

Limiting behaviour of atomic wave functions for large atomic number. IlI

1959 ◽  
Vol 251 (1267) ◽  
pp. 534-535 ◽  
Keyword(s):  
Wave Function ◽  
Atomic Number ◽  
Radial Wave Function ◽  
Wave Functions ◽  
Radial Wave ◽  
Atomic Wave ◽  
Large Atomic Number ◽  
Limiting Behaviour ◽  
The Mean

Results for the limiting screening number as N -> oo of an electron in the ( nl ) radial wave function of an atom with atomic number N , are extended to configurations including (4 s ), (4 p ) and (4 d ) electrons. The limiting slope of the screening number as a function of the mean radius of the wave function is given for the (4 s ) 2 (4 p ) 6 configuration.

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