Skip to main content
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 660
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Austen, Kat F. 2016. Theory Choice in the History of Chemical Practices.

    Fischetti, Massimo V. and Vandenberghe, William G. 2016. Advanced Physics of Electron Transport in Semiconductors and Nanostructures.

    Friedrich, Bretislav 2016. Wie kam der Baum des Wissens zur Blüte? Der Aufstieg der physikalischen und theoretischen Chemie, mit besonderem Augenmerk auf Berlin und Leipzig. Angewandte Chemie, Vol. 128, Issue. 18, p. 5466.

    Friedrich, Bretislav 2016. How Did the Tree of Knowledge Get Its Blossom? The Rise of Physical and Theoretical Chemistry, with an Eye on Berlin and Leipzig. Angewandte Chemie International Edition, Vol. 55, Issue. 18, p. 5378.

    Garbrecht, Björn and Millington, Peter 2016. Constraining the effective action by a method of external sources. Nuclear Physics B, Vol. 906, p. 105.

    Hadji, Djebar and Rahmouni, Ali 2016. Molecular structure, linear and nonlinear optical properties of some cyclic phosphazenes: A theoretical investigation. Journal of Molecular Structure, Vol. 1106, p. 343.

    Lee, June Gunn 2016. Trends in Computational Materials Science Based on Density Functional Theory. Journal of the Korean Ceramic Society, Vol. 53, Issue. 2, p. 184.

    Li Manni, Giovanni Smart, Simon D. and Alavi, Ali 2016. Combining the Complete Active Space Self-Consistent Field Method and the Full Configuration Interaction Quantum Monte Carlo within a Super-CI Framework, with Application to Challenging Metal-Porphyrins. Journal of Chemical Theory and Computation, Vol. 12, Issue. 3, p. 1245.

    Liu, Ji-Cai Berrah, Nora Cederbaum, Lorenz S Cryan, James P Glownia, James M Schafer, Kenneth J and Buth, Christian 2016. Rate equations for nitrogen molecules in ultrashort and intense x-ray pulses. Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 49, Issue. 7, p. 075602.

    Matczak, Piotr 2016. A Test of Various Partial Atomic Charge Models for Computations on Diheteroaryl Ketones and Thioketones. Computation, Vol. 4, Issue. 1, p. 3.

    Mustroph, Heinz 2016. Potential-Energy Surfaces, the Born-Oppenheimer Approximations, and the Franck-Condon Principle: Back to the Roots. ChemPhysChem,

    Oriols, X. 2016. Can decoherence make quantum theories unfalsifiable? Understanding the quantum-to-classical transition without it. Journal of Physics: Conference Series, Vol. 701, p. 012004.

    Ortmann, Roman Pasel, Christoph Luckas, Michael Heimböckel, Ruben Kraas, Sebastian Bentgens, Jürgen Fröba, Michael and Bathen, Dieter 2016. Adsorption and Desorption of Isoflurane on Carbonaceous Adsorbents and Zeolites at Low Concentrations in Gas Phase. Journal of Chemical & Engineering Data, Vol. 61, Issue. 1, p. 686.

    Rusakov, Alexander A. and Zgid, Dominika 2016. Self-consistent second-order Green’s function perturbation theory for periodic systems. The Journal of Chemical Physics, Vol. 144, Issue. 5, p. 054106.

    Ryde, U. 2016.

    Ryde, Ulf and Söderhjelm, Pär 2016. Ligand-Binding Affinity Estimates Supported by Quantum-Mechanical Methods. Chemical Reviews, Vol. 116, Issue. 9, p. 5520.

    Sazhin, S.S. Gun’ko, V.M. and Nasiri, R. 2016. Quantum-chemical analysis of the processes at the surfaces of Diesel fuel droplets. Fuel, Vol. 165, p. 405.

    Schöne, Florian Krüger, Sjard-Ole Grünwald, Peter Aßmann, Marc Heckötter, Julian Thewes, Johannes Stolz, Heinrich Fröhlich, Dietmar Bayer, Manfred and Scheel, Stefan 2016. Coupled valence band dispersions and the quantum defect of excitons in Cu2O. Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 49, Issue. 13, p. 134003.

    Sellier, J.M. and Dimov, I. 2016. On a full Monte Carlo approach to quantum mechanics. Physica A: Statistical Mechanics and its Applications, Vol. 463, p. 45.

    Sellier, J.M. Sviercoski, R.F. and Dimov, I. 2016. On the Wigner Monte Carlo method coupled to pseudopotential models. Journal of Computational and Applied Mathematics, Vol. 293, p. 217.

  • Mathematical Proceedings of the Cambridge Philosophical Society, Volume 24, Issue 1
  • January 1928, pp. 89-110

The Wave Mechanics of an Atom with a Non-Coulomb Central Field. Part I. Theory and Methods

  • D. R. Hartree (a1)
  • DOI:
  • Published online: 24 October 2008

The paper is concerned with the practical determination of the characteristic values and functions of the wave equation of Schrodinger for a non-Coulomb central field, for which the potential is given as a function of the distance r from the nucleus.

The method used is to integrate a modification of the equation outwards from initial conditions corresponding to a solution finite at r = 0, and inwards from initial conditions corresponding to a solution zero at r = ∞, with a trial value of the parameter (the energy) whose characteristic values are to be determined; the values of this parameter for which the two solutions fit at some convenient intermediate radius are the characteristic values required, and the solutions which so fit are the characteristic functions (§§ 2, 10).

Modifications of the wave equation suitable for numerical work in different parts of the range of r are given (§§ 2, 3, 5), also exact equations for the variation of a solution with a variation in the potential or of the trial value of the energy (§ 4); the use of these variation equations in preference to a complete new integration of the equation for every trial change of field or of the energy parameter avoids a great deal of numerical work.

For the range of r where the deviation from a Coulomb field is inappreciable, recurrence relations between different solutions of the wave equations which are zero at r = ∞, and correspond to terms with different values of the effective and subsidiary quantum numbers, are given and can be used to avoid carrying out the integration in each particular case (§§ 6, 7).

Formulae for the calculation of first order perturbations due to the relativity variation of mass and to the spinning electron are given (§ 8).

The method used for integrating the equations numerically is outlined (§ 9).

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
Please enter your name
Please enter a valid email address
Who would you like to send this to? *