Confined helium atom low-lying S states analyzed through correlated Hylleraas wave functions and the Kohn-Sham model

2006 ◽  
Vol 124 (5) ◽  
pp. 054311 ◽  
Author(s):  
N. Aquino ◽  
Jorge Garza ◽  
A. Flores-Riveros ◽  
J. F. Rivas-Silva ◽  
K. D. Sen
Keyword(s):  
Helium Atom ◽  
Wave Functions ◽  
S States

Variational energies for highly excited states of the helium atom

1978 ◽  
Vol 56 (6) ◽  
pp. 884-889 ◽  
Author(s):  
Wai-Tak Ma ◽  
Mary Kuriyan ◽  
Huw O. Pritchard
Keyword(s):  
Helium Atom ◽  
Excited States ◽  
Wave Functions ◽  
Experimental Results ◽  
New States ◽  
Variational Wave Functions ◽  
Variational Wave ◽  
S States

The efficient correlated variational wave functions used previously to study the higher 1 sns states of helium have been extended to other states of the helium atom, 1 snp (n ≤ 23), 2pnp1P (n ≤ 25), and 2pnp3P (n ≤ 25); similar uncorrelated wave functions were used for 1snd (n ≤ 21), 2pnp1D (n ≤ 10), and 2pnp3D (n ≤ 10). Attempts to use the same techniques for the 2pnp1,3S states appear to converge variationally to the energies of the 2s21S and 2s3s3S states respectively. Comparison is made with experimental results where appropriate, and agreement is excellent except in the case of the 1snd states above n = 13.A search was made for excited states of H− in each of these configurations, but no new states were found.

A comparison of wave functions for the normal helium atom

1937 ◽  
Vol 33 (2) ◽  
pp. 253-259 ◽  
Author(s):  
T. D. H. Baber ◽  
H. R. Hassé
Keyword(s):  
Magnetic Susceptibility ◽  
Helium Atom ◽  
Special Interest ◽  
Wave Functions ◽  
Electric Polarizability ◽  
Made In

The object of this paper is to compare some of the wave functions which have been suggested for the normal helium atom, including one calculated in the first section of the paper, as regards energy, magnetic susceptibility and electric polarizability. Since this atom provides the simplest two-electron problem, such a comparison is of special interest and may indicate the direction in which improvements might be made in the calculation of wave functions for more complicated atoms.

Analytic correlated wave functions in momentum space of excited S -states of Helium like Ions

1997 ◽  
Vol 39 (2) ◽  
pp. 101-107 ◽  
Author(s):  
F. Arias de Saavedra ◽  
E. Buendía ◽  
F. J. Gálvez
Keyword(s):  
Momentum Space ◽  
Wave Functions ◽  
S States

Correlated Atomic Pair Functions by the e-ϱ-Method. I. Ground State 11S and Lowest Excited States n1S (n > 1) and n3S of Helium

1999 ◽  
Vol 54 (12) ◽  
pp. 711-717
Author(s):  
F. F. Seelig ◽  
G. A. Becker
Keyword(s):  
Integral Equation ◽  
Wave Function ◽  
Helium Atom ◽  
Excited States ◽  
Ground State ◽  
Single Parent ◽  
Hartree Fock ◽  
Atomic Pair ◽  
Electronic Wave Function ◽  
S States

Abstract Some low n1S and n3S states of the helium atom are computed with the aid of the e-e method which formulates the electronic wave function of the 2 electrons ψ = e-e F, where ϱ=Z(r1+r2)–½r12 and here Z = 2. Both the differential and the integral equation for F contain a pseudopotential Ṽ instead of the true potential V that contrary to V is finite. For the ground state, F = 1 yields nearly the Hartree-Fock SCF accuracy, whereas a multinomial expansion in r1, r2 , r2 yields a relative error of about 10-7 . All integrals can be computed analytically and are derived from one single “parent” integral.

Series wave functions for the helium atom

2009 ◽  
Vol 24 (S17) ◽  
pp. 217-225
Author(s):  
C. L. Davis ◽  
E. N. Maslen
Keyword(s):  
Helium Atom ◽  
Wave Functions

Stationary properties of approximate wave functions

1969 ◽  
Vol 47 (21) ◽  
pp. 2355-2361 ◽  
Author(s):  
A. R. Ruffa
Keyword(s):  
Wave Function ◽  
Total Energy ◽  
Helium Atom ◽  
Wave Functions ◽  
Quantum Mechanical ◽  
Mechanical Wave ◽  
Expectation Value ◽  
Charge Densities ◽  
Hartree Fock ◽  
Approximate Wave

The accuracy of quantum mechanical wave functions is examined in terms of certain stationary properties. The most elementary of these, namely that displayed by the class of wave functions which yields a stationary value for the total energy of the system, is demonstrated to necessarily require few other stationary properties, and none of these appear to be particularly useful. However, the class of wave functions which yields both stationary energies and charge densities has very important stationary properties. A theorem is proven which states that any wave function in this class yields a stationary expectation value for any operator which can be expressed as a sum of one-particle operators. Since the Hartree–Fock wave function is known to possess these same stationary properties, this theorem demonstrates that the Hartree–Fock wave function is one of the infinitely many wave functions of the class. Methods for generating other wave functions in this class by modifying the Hartree–Fock wave function without changing its stationary properties are applied to the calculation of wave functions for the helium atom.

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