Stability of One–Electron Molecules in the Brown–Ravenhall Model
نویسندگان
چکیده
In appropriate units, the Brown-Ravenhall Hamiltonian for a system of 1 electron relativistic molecules with K fixed nuclei having charge and position Zk, Rk, k = 1, 2, . . . ,K, is of the form B1,K = Λ+ ( D0 + αVc ) Λ+, where Λ+ is the projection onto the positive spectral subspace of the free Dirac operator D0 and Vc = − ∑K k=1 αZk |x−Rk| + ∑K k<l, k,l=1 αZkZl |Rk−Rl| , with α Sommerfeld’s fine structure constant. It is proved that for αZk ≤ αZc = 2 π/2+2/π , k = 1, 2, . . . ,K, B1,K ≥ const·K.
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