By Harald Friedrich
This tested textual content comprises a sophisticated presentation of quantum mechanics tailored to the necessities of recent atomic physics. The 3rd variation extends the profitable moment variation with an in depth remedy of the wave movement of atoms, and it additionally comprises an creation to a couple features of atom optics that are proper for present and destiny experiments related to ultra-cold atoms. incorporated: numerous issues of entire ideas.
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Extra resources for Theoretical Atomic Physics, 3rd edition
Sample text
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 . . , and the corresponding energy eigenvalues are R . 102). Similar to the radially symmetric harmonic oscillator (see Sect. 3 Bound States and Unbound States 25 a Coulomb potential have an additional degeneracy, which is expressed in the present case by the fact that they do not depend on the angular momentum quantum number l; values of l are however restricted to be smaller than n.
160), but stationary solutions of the Schr¨ odinger equaton including the potential V (x). 171) with the appropriate wave number k. 160). e. 177) corresponding to a rightward travelling incoming√par∆k = 1/(β 2) – ticle. 4. 176). Furthermore, the reflected-wave part proportional to e−ikx yields negligible contributions. 176); for very large values of |x| this oscillates extremely rapidly, because k0 + k is always a positive number larger than k0 , and these oscillations suppress the contributions to the integral.
Assume for ˆ Y , which act only on ˆ consists of the operators H ˆ X and H example, that H functions of X and Y respectively, together with a simple coupling potential given by the function V (X, Y ): ˆ =H ˆX + H ˆ Y + V (X, Y ) . 208) ˆ Y may be used to define channels. 209) m=n. 212) corresponding to the internal energy of the Y variables in the respective channels. To be even more precise let us assume that ψ(X, Y ) describes a point particle of mass µ moving in an effective radial potential Veff (r) and interacting with a number of other bound particles.