Marek Gruchowski and Radosław Szmytkowski 2004 J. Phys. A: Math. Gen. 37 7783 doi:10.1088/0305-4470/37/31/010
The finite-volume Dirac–Hartree–Fock method for confined relativistic many-electron systems
Marek Gruchowski and Radosław Szmytkowski
Show affiliationsAn energy eigenproblem for a relativistic N-electron system confined to the interior of a finite volume 
is considered. The confinement is modelled by imposing a local impedance boundary condition at a hypersurface enclosing the hypervolume 
in the configuration space. It is shown that energy eigenvalues are non-increasing functions of the hypersurface impedance. Variational principles for energy eigenvalues, admitting the use of trial functions which do not obey the boundary condition imposed on exact eigenfunctions, are constructed in a systematic manner. The Dirac–Hartree–Fock method is applied to derive integro-differential equations and local boundary conditions satisfied by one-electron spin orbitals from which the best determinantal approximations to exact eigenfunctions are built. It is proved that the Dirac–Hartree–Fock estimates of exact energy eigenvalues are also non-increasing functions of the hypersurface impedance.
- PACS
- MSC
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45K05 Integro-partial differential equations (See also 34K30, 35R10, 47G20)
49R50 Variational methods for eigenvalues of operators (See also 47A75)
- Subjects
- Dates
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Issue 31 (6 August 2004)
Received 14 April 2004, in final form 17 June 2004
Published 21 July 2004
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The finite-volume Dirac–Hartree–Fock method for confined relativistic many-electron systems
Marek Gruchowski and Radosław Szmytkowski 2004 J. Phys. A: Math. Gen. 37 7783
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