Wellenmechanik und halbzahlige Quantisierung

Wave reflection and quasiresonance

“…For potentials of the type described, the scattering coefficients in (26) can be represented exactly in the form is so large that i/k + limit > 0 as k * me The latter case is quasiclassical, the third turning point, r 0 , is a simple one, near which the solution of (21) is close to an Airy function, the condition of square integrability picks out the correct Airy function, and the well-known solution [Kramers 1926, Olver 1974] of the WKB-connection problem for such a simple turning point yields…”

Deep nuclear resonant tunneling thermal rate constant calculations

“…A JWKB (Jeffreys-Wenzel-Brillouin-Kramer) [66][67][68][69] derivation of the BW distribution for these resonance peaks is given in App. B. Consequently, we corrected our "ODE method" using an analytical expression for the transmission probability at the center of the narrowest peaks.…”

Single molecule charge transport: from a quantum mechanical to a classical description

“…However, it is interesting to first consider the reasons behind the transition from a quantum mechanical to a classical description (beyond the superficial, albeit intuitive, connection that follows from the Ehrenfest theorem 28,29 or from the WKB approximation). [29][30][31][32] This issue was originally treated in the context of quantum measurement and quantum information theory. While a detailed consideration of the subject is beyond the scope of this paper (comprehensive reviews can be found in ref.…”

“…In this case one speaks of a polaron, a self-induced localized state of the charge carrier. The degree of localization, in the sense of eqn (31), depends on the relative magnitude of the electronic couplings J and the reorganization energy l of the environment due to polarization by the charge carrier. If l c J, the charge carrier is almost completely localized on a single molecular unit and is referred to as a ''small'' polaron.…”