93,213 research outputs found
On the virial theorem for the relativistic operator of Brown and Ravenhall, and the absence of embedded eigenvalues
A virial theorem is established for the operator proposed by Brown and
Ravenhall as a model for relativistic one-electron atoms. As a consequence, it
is proved that the operator has no eigenvalues greater than , where is the fine structure constant, for
all values of the nuclear charge below the critical value : in
particular there are no eigenvalues embedded in the essential spectrum when . Implications for the operators in the partial wave
decomposition are also described.Comment: To appear in Letters in Math. Physic
Trace-scaling automorphisms of certain stable AF algebras
Trace scaling automorphisms of stable AF algebras with dimension group
totally ordered are outer conjugate if the scaling factors are the same (not
equal to one). This is an adaptation of a similar result for the AFD type
II_infty factor by Connes and extends the previous result for stable UHF
algebras.Comment: 12 pages, late
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