By C. J. Pethick, H. Smith

In 1925 Einstein expected that at low temperatures debris in a gasoline might all stay within the similar quantum kingdom. This gaseous nation, a Bose-Einstein condensate, was once produced within the laboratory for the 1st time in 1995 and investigating such condensates is likely one of the such a lot energetic parts in modern physics. The authors of this graduate-level textbook clarify this fascinating new topic when it comes to simple actual rules, with no assuming distinctive previous wisdom. Chapters hide the statistical physics of trapped gases, atomic homes, cooling and trapping atoms, interatomic interactions, constitution of trapped condensates, collective modes, rotating condensates, superfluidity, interference phenomena, and trapped Fermi gases. challenge units also are integrated.

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22) where f¯ = ω ¯ /2π. For a uniform Bose gas in a three-dimensional box of volume V , corresponding to α = 3/2, the constant C3/2 is given by Eq. 23) where n = N/V is the number density. 17) diverges. Thus Bose–Einstein condensation in a two-dimensional box can occur only at zero temperature. However, a two-dimensional Bose gas can condense at non-zero temperature if the particles are conﬁned by a harmonic-oscillator potential. 17) is ﬁnite. We shall return to gases in lower dimensions in Sec.

14). 1. The gamma function Γ and the Riemann zeta function ζ for selected values of α. 082 √ is the geometric mean of the three oscillator frequencies. 22) where f¯ = ω ¯ /2π. For a uniform Bose gas in a three-dimensional box of volume V , corresponding to α = 3/2, the constant C3/2 is given by Eq. 23) where n = N/V is the number density. 17) diverges. Thus Bose–Einstein condensation in a two-dimensional box can occur only at zero temperature. However, a two-dimensional Bose gas can condense at non-zero temperature if the particles are conﬁned by a harmonic-oscillator potential.

3) Alkali and hydrogen atoms in their ground states have J = S = 1/2. The splitting between the levels F = I + 1/2 and F = I − 1/2 is therefore given by 1 ∆Ehf = hνhf = (I + )A. 1. As a speciﬁc example, consider an alkali atom with I = 3/2 in its ground state (J = S = 1/2). The quantum number F may be either 1 or 2, and I·J = −5/4 and 3/4, respectively. The corresponding shifts of the ground-state multiplet are given by E1 = −5A/4 (three-fold degenerate) and E2 = 3A/4 (ﬁve-fold degenerate). 4).