Coordinate representation of the McWeeny-Coulson wave function for the helium atom

Numerical modeling of the deuteron wave function in the coordinate representation for the phenomenological nucleon–nucleon potential Argonne v18 has been performed. For this purpose, the asymptotic behavior of the radial wave function has been taken into account near the origin of coordinates and at infinity. The charge deuteron form factor [Formula: see text], depending on the transmitted momentums up to [Formula: see text], has been calculated employing five models for the deuteron wave function. A characteristic difference in calculations of [Formula: see text] is observed near the positions of the first and second zero. The difference between the obtained values for [Formula: see text] form factor has been analyzed using the values of the ratios and differences for the results. Obtained outcomes for charge deuteron form factor at large momentums may be a prediction for future experimental data.

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Calculation of atomic scattering factors for the helium atom by means of the six-term Hylleraas wave function

Acta Crystallographica ◽

10.1107/s0365110x63002462 ◽

1963 ◽

Vol 16 (9) ◽

pp. 926-928 ◽

Cited By ~ 2

Author(s):

M. L. Rustgi ◽

M. M. Shukla ◽

A. N. Tripathi

Keyword(s):

Wave Function ◽

Helium Atom ◽

Atomic Scattering

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Highly excited 1sns states of the helium atom

Canadian Journal of Chemistry ◽

10.1139/v76-222 ◽

1976 ◽

Vol 54 (10) ◽

pp. 1543-1549 ◽

Cited By ~ 1

Author(s):

Mary Kuriyan ◽

Huw O. Pritchard

Keyword(s):

Wave Function ◽

Helium Atom ◽

Lower Energy ◽

Computer Time ◽

Suitable Choice ◽

Triplet States ◽

Astrophysical Interest ◽

Variational Calculations ◽

Singlet And Triplet States

Variational calculations are reported on the 1sns singlet and triplet states of the helium atom, up to and including n = 26. By suitable choice of terms in the expansion for the wave function, significant economies in computer time are possible, and we quote an example of a 12-term uncorrelated wave function which gives a lower energy than Pekeris' 220-term correlated wave function. The problems of extending these calculations to much higher n (e.g. n > 100) to include states of astrophysical interest are enumerated.

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

Zeitschrift für Naturforschung A ◽

10.1515/zna-1999-1209 ◽

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.

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Stationary properties of approximate wave functions

Canadian Journal of Physics ◽

10.1139/p69-287 ◽

1969 ◽

Vol 47 (21) ◽

pp. 2355-2361 ◽

Cited By ~ 1

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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