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

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

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.

CALCULATION OF THEORETICAL ISOTROPIC COMPTON PROFILE FOR MANY PARTICLE SYSTEMS

2010 ◽  
Vol 24 (14) ◽  
pp. 1601-1614
Author(s):  
ALI A. ALZUBADI ◽  
KHALIL H. ALBAYATI
Keyword(s):  
Wave Function ◽  
Impulse Approximation ◽  
Particle Systems ◽  
Electron Interaction ◽  
Compton Profile ◽  
High Momentum ◽  
Atomic Systems ◽  
Hartree Fock ◽  
Hf Wave ◽  
Momentum Region

Theoretical isotropic (spherically symmetric) Compton profiles (ICP) have been calculated for many particle systems' He , Li , Be and B atoms in their ground states. Our calculations were performed using Roothan–Hartree–Fock (RHF) wave function, HF wave function of Thakkar and re-optimized HF wave function of Clementi–Roetti, taking into account the impulse approximation. The theoretical analysis included a decomposition of the various intra and inter shells and their contributions in the total ICP. A high momentum region of up to 4 a.u. was investigated and a non-negligible tail was observed in all ICP curves. The existence of a high momentum tail was mainly due to the electron–electron interaction. The ICP for the He atom has been compared with the available experimental data and it is found that the ICP values agree very well with them. A few low order radial momentum expectation values 〈pn〉 and the total energy for these atomic systems have also been calculated and compared with their counterparts' wave functions.

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.

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

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.

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