Concentration of hemoglobin and hematocrit in schoolchildren, Campinas, São Paulo, Brazil

A family of exact eigenstates for a single trapped ion interacting with a laser field

“…Note now that, when δ = 0 equations (14) and (19) coincide, and thus, ψ m± ion are simultaneous (in fact, degenerate) eigenstates for any combination of Ω, η at which det M ± m = 0. Another way of understanding this fact is to note that the ion-trap Hamiltonian H ion has in this case an extra symmetry: it commutes with the parity-like observable σ x exp(iπa † a) (in the JCM picture, the corresponding symmetry operator is σ z exp(iπa † a)).…”

A family of exact eigenstates for a single trapped ion interacting with a laser field

“…Note in particular that, when |δ| = kν for integer k, all but k of these energy levels are degenerate. In the special case δ = 0 it can in fact be shown from symmetry considerations alone that the entire asymptotic spectrum must be two-fold degenerate [19]). Conversely, no such asymptotic degeneracies occur for |δ| = kν.…”

“…19) coincide, and thus, ψ m± ion are simultaneous (in fact, degenerate) eigenstates for any combination of Ω, η at which det M ± m = 0. Another way of understanding this fact is to note that the ion-trap Hamiltonian H ion has in this case an extra symmetry: it commutes with the parity-like observable σ x exp(iπa † a) (in the JCM picture, the corresponding symmetry operator is σ z exp(iπa † a)).…”