BLOCK-DIAGONALIZATION OF OPERATORS WITH GAPS, WITH APPLICATIONS TO DIRAC OPERATORS
2012 ◽
Vol 24
(08)
◽
pp. 1250021
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Keyword(s):
We present new results on the block-diagonalization of operators with spectral gaps, based on a method of Langer and Tretter, and apply them to Dirac operators on three-dimensional Euclidean space with unbounded potentials. For the Coulomb potential, we achieve an exact diagonalization up to nuclear charge Z = 124 (which covers all chemical elements) and prove the convergence of an approximate block-diagonalization up to Z = 62, thus considerably improving the upper bounds Z = 93 and Z = 51, respectively, established by Siedentop and Stockmeyer.
2000 ◽
Vol 15
(25)
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pp. 1577-1581
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Keyword(s):
2008 ◽
Vol 17
(4)
◽
pp. 619-625
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Keyword(s):
1956 ◽
Vol 8
◽
pp. 256-262
◽
1993 ◽
Vol 304
(3-4)
◽
pp. 256-262
◽
Keyword(s):
1963 ◽
Vol 15
◽
pp. 157-168
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Keyword(s):