Helium Wave Function in Momentum Space

1960 ◽  
Vol 120 (1) ◽  
pp. 150-152 ◽  
Author(s):  
M. G. Henderson ◽  
Charles W. Scherr
Keyword(s):  
Wave Function ◽  
Momentum Space

Impact Parameter Representations

1972 ◽  
Vol 50 (16) ◽  
pp. 1862-1875 ◽  
Author(s):  
A. N. Kamal
Keyword(s):  
Wave Function ◽  
Impact Parameter ◽  
Momentum Space ◽  
Scattering Amplitude ◽  
Function Approach ◽  
Coordinate Space ◽  
Energy Shell ◽  
Parameter Representation ◽  
The Relationship

A discussion of the Glauber and Blankenbecler–Goldberger impact parameter representation for the scattering amplitude is presented with emphasis on the wave function approach. The treatment makes clear the relationship between the approximations made to derive either of the two amplitudes. Both on-energy-shell and off-energy-shell scatterings are treated. A derivation of the two representations in momentum space is presented bringing out the relationship between the approximations in a coordinate space treatment and the momentum space treatment.

scholarly journals On the Canonical Transformation of Time-Dependent Harmonic Oscillator

2010 ◽  
Vol 2010 ◽  
pp. 1-4
Author(s):  
Akpan N. Ikot ◽  
Louis E. Akpabio ◽  
Ita O. Akpan ◽  
Michael I. Umo ◽  
Oladunjoye A. Awoga ◽  
...  
Keyword(s):  
Wave Function ◽  
Harmonic Oscillator ◽  
Canonical Transformation ◽  
Momentum Space ◽  
Hamiltonian Operator ◽  
Momentum Operator ◽  
Time Dependent ◽  
Variable Transformation ◽  
Time Coordinate ◽  
Space Coordinate

We performed a two-variable canonical transformation on the time momentum operator, and without loss of generality we carried out a three-variable transformation on the coordinate and momentum space operators to trivialize the Hamiltonian operator of the system. Fortunately, this operation separates the time-coordinate and space coordinate naturally, and the wave function of the time-dependent Harmonic Oscillator is evaluated via the generator.

Erratum: Helium momentum-space wave function and Compton profile

1991 ◽  
Vol 44 (1) ◽  
pp. 796-796 ◽  
Author(s):  
Paul J. Schreiber ◽  
R. P. Hurst ◽  
Thomas E. Duvall
Keyword(s):  
Wave Function ◽  
Momentum Space ◽  
Compton Profile ◽  
Momentum Space Wave Function ◽  
Space Wave

Helium momentum-space wave function and Compton profile

1988 ◽  
Vol 38 (7) ◽  
pp. 3200-3209 ◽  
Author(s):  
Paul J. Schreiber ◽  
R. P. Hurst ◽  
Thomas E. Duvall
Keyword(s):  
Wave Function ◽  
Momentum Space ◽  
Compton Profile ◽  
Momentum Space Wave Function ◽  
Space Wave

On the time-dependent Rindler Hamiltonian single particle eigenstates in momentum space

2020 ◽  
Vol 35 (11) ◽  
pp. 2050075
Author(s):  
Soma Mitra ◽  
Sanchita Das ◽  
Somenath Chakrabarty
Keyword(s):  
Wave Function ◽  
Time Evolution ◽  
Laplace Equation ◽  
Momentum Space ◽  
Evolution Equations ◽  
Polar Coordinates ◽  
Mathematical Explanation ◽  
Initial Time ◽  
Unruh Effect ◽  
Momentum Space Wave Function

We have developed a formalism in the non-relativistic scenario to obtain the time evolution of the eigenstates of Rindler Hamiltonian in momentum space. Hence, the particle wave function in spacetime coordinates is obtained using Fourier transform of the momentum space wave function. We have discussed the difficulties with characteristic curves, and re-cast the time evolution equations in the form of two-dimensional Laplace equation. The solutions are obtained both in polar coordinates as well as in the Cartesian form. It has been observed that in the Cartesian coordinate, the probability density is zero both at [Formula: see text] (the initial time) and at [Formula: see text] (the final time) for a given [Formula: see text]-coordinate. The reason behind such peculiar behavior of the eigenstate is because it satisfies (1 + 1)-dimensional Laplace equation. This is of course the mathematical explanation, whereas physically we may interpret that it is because of the Unruh effect.

The (e, 2e) reaction in molecules: Momentum space wave function of H2

1973 ◽  
Vol 44 (7) ◽  
pp. 531-532 ◽  
Author(s):  
E. Weigold ◽  
S.T. Hood ◽  
I.E. McCarthy ◽  
P.J.O. Teubner
Keyword(s):  
Wave Function ◽  
Momentum Space ◽  
Momentum Space Wave Function ◽  
Space Wave

scholarly journals On duality of color and kinematics in (A)dS momentum space

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Soner Albayrak ◽  
Savan Kharel ◽  
David Meltzer
Keyword(s):  
Wave Function ◽  
Analytic Continuation ◽  
Momentum Space ◽  
Spectral Representation ◽  
Flat Space ◽  
Tree Level ◽  
De Sitter ◽  
Yang Mills ◽  
The Universe ◽  
Double Copy

Abstract We explore color-kinematic duality for tree-level AdS/CFT correlators in momentum space. We start by studying the bi-adjoint scalar in AdS at tree-level as an illustrative example. We follow this by investigating two forms of color-kinematic duality in Yang-Mills theory, the first for the integrated correlator in AdS4 and the second for the integrand in general AdSd+1. For the integrated correlator, we find color-kinematics does not yield additional relations among n-point, color-ordered correlators. To study color-kinematics for the AdSd+1 Yang-Mills integrand, we use a spectral representation of the bulk-to-bulk propagator so that AdS diagrams are similar in structure to their flat space counterparts. Finally, we study color KLT relations for the integrated correlator and double-copy relations for the AdS integrand. We find that double-copy in AdS naturally relates the bi-adjoint theory in AdSd+3 to Yang-Mills in AdSd+1. We also find a double-copy relation at three-points between Yang-Mills in AdSd+1 and gravity in AdSd−1 and comment on the higher-point generalization. By analytic continuation, these results on AdS/CFT correlators can be translated into statements about the wave function of the universe in de Sitter.

scholarly journals Uncertainty Relations in the Madelung Picture

Entropy ◽  
2021 ◽  
Vol 24 (1) ◽  
pp. 20
Author(s):  
Moise Bonilla-Licea ◽  
Dieter Schuch
Keyword(s):  
Wave Function ◽  
Quantum System ◽  
Momentum Space ◽  
Coherent States ◽  
Quantum Mechanical ◽  
Uncertainty Relations ◽  
Hydrodynamic Equations ◽  
Generalized Coherent States ◽  
Complex Wave ◽  
Classical Hydrodynamic

Madelung showed how the complex Schrödinger equation can be rewritten in terms of two real equations, one for the phase and one for the amplitude of the complex wave function, where both equations are not independent of each other, but coupled. Although these equations formally look like classical hydrodynamic equations, they contain all the information about the quantum system. Concerning the quantum mechanical uncertainties of position and momentum, however, this is not so obvious at first sight. We show how these uncertainties are related to the phase and amplitude of the wave function in position and momentum space and, particularly, that the contribution from the phase essentially depends on the position–momentum correlations. This will be illustrated explicitly using generalized coherent states as examples.

A HADRON–QUARK VERTEX FUNCTION: INTERCONNECTION BETWEEN 3D AND 4D WAVE FUNCTIONS

1992 ◽  
Vol 07 (01) ◽  
pp. 121-134 ◽  
Author(s):  
A. N. MITRA ◽  
S. BHATNAGAR
Keyword(s):  
Wave Function ◽  
Momentum Space ◽  
Vertex Function ◽  
Mass Spectra ◽  
Mass Shell ◽  
Wave Functions ◽  
Invariant Form ◽  
Quark Loop ◽  
Transition Amplitudes

The interrelation between the 4D and 3D forms of the Bethe–Salpeter equation (BSE) with a kernel [Formula: see text] which depends on the relative four-momenta, [Formula: see text] orthogonal to Pμ is exploited to obtain a hadron–quark vertex function of the Lorentz-invariant form [Formula: see text]. The denominator function [Formula: see text] is universal and controls the 3D BSE, which provides the mass spectra with the eigenfunctions [Formula: see text]. The vertex function, directly related to the 4D wave function Ψ which satisfies a corresponding BSE, defines a natural off-shell extension over the whole of four-momentum space, and provides the basis for the evaluation of transition amplitudes via appropriate quark-loop digrams. The key role of the quantity [Formula: see text] in this formalism is clarified in relation to earlier approaches, in which the applications of this quantity had mostly been limited to the mass shell (q · P = 0). Two applications (fP values for [Formula: see text] and Fπ for π0 → γγ) are sketched as illustrations of this formalism, and attention is drawn to the problem of complex amplitudes for bigger quark loops with more hadrons, together with the role of the [Formula: see text] function in overcoming this problem.

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