By Harald Siegfried Friedrich

This tested textual content includes a complicated presentation of quantum mechanics tailored to the necessities of recent atomic physics. The 3rd variation extends the winning moment version with an in depth remedy of the wave movement of atoms, and it additionally comprises an creation to a few points of atom optics that are appropriate for present and destiny experiments concerning ultra-cold atoms. incorporated: a variety of issues of whole solutions.

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216). 223) i=1 j=1 If they are normalized to unity we have (1j1(k)11j1(1)) = Dk,l , (1j1(k)lifI1j1(1») = ckDk,l, k, 1= 1, ... N . 224) The method of diagonalizing in a subspace is particularly useful if we are looking for approximations to describe not only the ground state of a system. 215) sets an upper bound for the ground state energy and hence we know, the lower the value of E[ 1j1], the closer it is to the exact ground state energy El. 215), and it is not always a good thing to approximate it by a model state with as Iowan energy as possible.

178). This additional phase shift characterizes the resonance. 179) for tan 8. e. 182) 36 1. Review of Quantum Mechanics 2 Fig. 8. 183». :1. Around the resonance energy ER the phase 8 rises more or less suddenly by 7r. 181); at E = ER - r and E = ER + r the phase has risen 1/4 and 3/4 of 7r respectively. 183) is illustrated for constant values of the parameters ER and r in Fig. 8. 183) is called a Breit-Wigner resonance. 183). 185). 4 Resonances and Channels 37 of the resonance. For a broader resonance, however, the unique definition of its position and width can become a difficult problem (see also Sect.

1. Around the resonance energy ER the phase 8 rises more or less suddenly by 7r. 181); at E = ER - r and E = ER + r the phase has risen 1/4 and 3/4 of 7r respectively. 183) is illustrated for constant values of the parameters ER and r in Fig. 8. 183) is called a Breit-Wigner resonance. 183). 185). 4 Resonances and Channels 37 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 coupled channel equations.