TY - JOUR

T1 - Spurious states of the dirac equation in a finite basis set

AU - Tupitsyn, I. I.

AU - Shabaev, V. M.

PY - 2008/8/1

Y1 - 2008/8/1

N2 - The occurrence of spurious states for the Dirac equation in a finite basis set is considered. For a Coulomb central-field potential, the spectra of the radial Dirac operator in a finite basis set (without using the kinetic balance) are shown to coincide for two different values of the relativistic quantum number κ that differ in sign. For an attractive Coulomb potential, this means that, for any basis set, spurious states p 1/2, d 3/2, ,..., (κ > 0) arise, whose energies exactly coincide with energies of the states 1s 1/2, 2p 3/2, ,..., (κ < 0), respectively. In addition, the negative spectra of the Dirac operator in a finite basis set for κ > 0 and κ < 0 also coincide.

AB - The occurrence of spurious states for the Dirac equation in a finite basis set is considered. For a Coulomb central-field potential, the spectra of the radial Dirac operator in a finite basis set (without using the kinetic balance) are shown to coincide for two different values of the relativistic quantum number κ that differ in sign. For an attractive Coulomb potential, this means that, for any basis set, spurious states p 1/2, d 3/2, ,..., (κ > 0) arise, whose energies exactly coincide with energies of the states 1s 1/2, 2p 3/2, ,..., (κ < 0), respectively. In addition, the negative spectra of the Dirac operator in a finite basis set for κ > 0 and κ < 0 also coincide.

UR - http://www.scopus.com/inward/record.url?scp=50249160570&partnerID=8YFLogxK

U2 - 10.1134/S0030400X08080043

DO - 10.1134/S0030400X08080043

M3 - Article

AN - SCOPUS:50249160570

VL - 105

SP - 183

EP - 188

JO - OPTICS AND SPECTROSCOPY

JF - OPTICS AND SPECTROSCOPY

SN - 0030-400X

IS - 2

ER -