By Erwin Madelung
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Extra info for Die mathematischen Hilfsmittel des Physikers
2 , of the wave function Ψ(1, 2, 3, . g. ). g. Ψ(1, 2, 3, . ) = Ψ(2, 1, 3, . g. Ψ(1, 2, 3, . ) = −Ψ(2, 1, 3, . ) for particles of half-integer spin, called fermions). 12 1 Basic Principles Summarized The probability of ﬁnding two or more identical fermions in the same orbital-spin state is zero. 10) means that at most two electrons (one with spin up and the other with spin down) can occupy the same orbital state. 5), and consequently, the basic principles of Chemistry is well-known. Perhaps not so well appreciated is its role in amplifying the kinetic energy of identical fermions sharing the same volume V .
The surface tension coefﬁcient, as , may also enter since the surface tension tends to minimize the surface, and consequently, tends to restore a ﬂat surface; however, this restoring force is insigniﬁcant in comparison with the gravitational force unless the wavelength is of the order of centimeters or less. The unit of absolute temperature can be produced from the unit of energy by dividing by kB , the Boltzmann’s constant. Length is produced by choosing ν = 1, μ = ξ = 0; time is produced by choosing μ = −1/2, ν = 1/2, and ξ = 0; ﬁnally mass is produced by choosing μ = 0, ν = 3, and ξ = 1.
16), we have ρe = const. × aB f e2 Z, ma T P , , ,... 43) If we make the assumptions that T and P do not play an important role, that the atomic mass is not so important,21 and that aB must be replaced everywhere by r¯α aB , we have ρe = const. × aB r¯a e2 20¯ ra μΩcm . 44) Thus, the dimensional analysis combined with the physical picture described in the footnote 21, estimates the electrical resistivity of solids to be of the order of 50 μΩ cm. This value is not far from the experimental values of ρe for certain metals at T = 295 K as shown in the following table.
Die mathematischen Hilfsmittel des Physikers by Erwin Madelung