By Harald Friedrich
This verified textual content includes a complicated presentation of quantum mechanics tailored to the necessities of contemporary atomic physics. The 3rd variation extends the profitable moment variation with an in depth remedy of the wave movement of atoms, and it additionally includes an creation to a few features of atom optics that are appropriate for present and destiny experiments regarding ultra-cold atoms. integrated: numerous issues of entire strategies.
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Extra info for Theoretical Atomic Physics, 3rd edition
Example text
The particle keeps its direction of motion and reflection is forbidden in the framework of classical mechanics. 173) need not vanish, however, and this process of classically forbidden reflection is called quantum reflection. 4 Processes Involving Unbound States 35 the subscript “r” reminds us that the incoming particle approaches from the right. 174) as ψr . Comparing the amplitudes of the transmitted and reflected waves gives the reciprocity relations, T . 173) for reflection do not depend on the side from which the incident particle approaches the interaction region.
233) is called a Breit-Wigner resonance. 234) and has a maximum at the resonance energy ER , with Γ =2 dδ dE −1 . 233). 235). 231) and also the background phase shift δbg can be regarded as constants over the whole width of the resonance. For a broader resonance, however, the unique definition of its position and width can become a difficult problem (see also Sect. 3). The derivative of the phase shift with respect to energy is also a measure for the strength of the closed-channel component in the solution of the coupledchannel equations.
2κr)−λ . (l − λ)! 44) of the functions Kl± 12 . We can venture one step further and allow the effective potential in the outer region to contain a long-ranged Coulomb contribution proportional to 1/r: Veff (r) = l(l + 1)¯ h2 C , − 2µr2 r r ≥ r0 . 5). At r = r0 we now match to the wave function φ− (r) = Wγ,l+ 12 (2κr) , which decreases exponentially for r → ∞. 100) ¯ 2κ h describes the relative strength of the 1/r term in the potential. The dependence of γ on energy E or on κ is determined by a length parameter a, γ= 1 .