Download Theoretical Atomic Physics by Harald Siegfried Friedrich PDF
By Harald Siegfried Friedrich
This demonstrated textual content includes a sophisticated presentation of quantum mechanics tailored to the necessities of recent atomic physics. The 3rd version extends the winning moment version with an in depth therapy of the wave movement of atoms, and it additionally includes an advent to a few facets of atom optics that are proper for present and destiny experiments related to ultra-cold atoms. incorporated: a variety of issues of whole solutions.
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Example text
JK5-K,2. 1). For finite angular momentum quantum number 1 > 0 the effective potential Yetr contains the centrifugal potential, and the regular solution in the inner region is 4>r~ro(r) = Kr j,(Kr) . 35) of the spherical Bessel functions. 122) in the absence of a centrifugal term, but the wave number in the inner region is now 24 1. 127) (see Fig. 3). 131) Attractive Coulomb Potential. g. for a hydrogen atom the square of the elementary electric charge, C = e2 • The bound states are characterized by a Coulomb principal quantum number, n = 1, 2, 3 ...
The bound states in a Coulomb potential do not form a complete set. 24). 2). The eigenfunctions in a Coulomb potential only become a complete set if we include the unbound states of the continuum E > O. The unbound eigenfunctions are just the regular Coulomb functions F/(T/, kr) introduced in Sect. 2. From 1. 4 we obtain the following fonnula for the behaviour of the regular Coulomb functions in an attractive Coulomb potential (TJ < 0) at small separations (r ~ 0) close to the continuum threshold (k ~ 0): ~ F/(TJ, kr) :::: (21!
2/ {I 1). 115) as a function of the energy E. 03 = = r to,--------------------------, o v -1 E 2 3 Fig. 10. The same as Fig. 0. 5 to neighbouring resonances), then the jump of the phase shift is well described by the arctan form of the Breit-Wigner resonance. For potential resonances such as those shown in Figs. 10 it is not so straightforward to decompose the total phase shift into a weakly energy-dependent background phase shift and a resonant part. As Fig. 183) would lead to expect. At energies above the resonances in Figs.