By P. W. Anderson
Philip W. Anderson is a theoretical physicist who has been defined because the so much imaginitive of condensed topic physicists operating this present day, or, on the other hand, because the "godfather' of the topic. His contributions as frequently set the schedule for others to paintings on as they represent particular discoveries. Examples of the previous are the Anderson version for magnetic impurities (cited for the Nobel Prize), the matter of spin glass and the popularity of the fluctuating valence challenge; of the latter superexchange, localization (a moment think about the Nobel Prize), codiscovery of the Josephson impact, prediction and microscopic rationalization of superfluidity in He-3, the 1st advice of the "Higgs" mechanism, the answer of the Kondo challenge, the mechanism of pulsar system faults, flux creep and movement in superconducting magnets, the microscopic mechanism of excessive Tec superconductivity, and extra. just a number of the subjects on which he has labored should be incorporated within the current quantity, which is composed basically of reprints of articles chosen for his or her value, their overview personality, or their unavailability. Professor Anderson has supplied short reviews on how every one got here to be written, in addition to an introductory essay giving his common perspective to the perform of technological know-how.
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To obtain the first-order s–yo relationship, we replace the second term on the left-hand side of Eq. 94) by the corresponding quantity for the planar case (Eq. 88)), namely, 2 dy 2 dy 2k ! 1=2 y f (u)du 0 ð1:101Þ 24 POTENTIAL AND CHARGE OF A HARD PARTICLE By expanding Eq. 101) with respect to 1/ka and retaining up to the first order of 1/ka, we have dy 2 ¼ Àkf (y) 1 þ dr kaf 2 (y) Z ! y ð1:102Þ f (u)du 0 From Eqs. 102) we obtain the first-order s–yo relationship, namely, er eo kkT 2 f (yo ) 1 þ s¼ e kaf 2 (yo ) Z !
140) as y ¼ yo y¼ for c ¼ 1 dy ¼0 ds for c ¼ 0 ð1:151Þ ð1:152Þ 34 POTENTIAL AND CHARGE OF A HARD PARTICLE In the limit ka ) 1, Eq. 148) reduces to c2 d2 y dy þ c ¼ sinh y dc2 dc ð1:153Þ with solution y(c) ¼ 2ln 1 þ tanh(yo =4)c 1 À tanh(yo =4)c ! ð1:154Þ an expression obtained by White . We note that from Eq. 1 and replacing H(y) in Eq. (148) by its large ka limiting form (Eq. 155)) we obtain c2 d2 y dy þ c ¼ sinh y À (1 À b2 )fsinh y À 2 sinh(y=2)g dc2 dc ð1:156Þ This equation can be integrated to give y(r) ¼ 2 ln (1 þ Dc)f1 þ ((1 À b)=(1 þ b))Dcg (1 À Dc)f1 À ((1 À b)=(1 þ b))Dcg !
The relative error of Eq. 206) is less than 1% for ka ! 1. 7 43 NEARLY SPHERICAL PARTICLE So far we have treated uniformly charged planar, spherical, or cylindrical particles. 5). In the following, we give an example in which one can derive approximate solutions. 9) for the potential distribution c(r) around a nearly spherical spheroidal particle immersed in an electrolyte solution . This method is based on Maxwell’s method  to derive an approximate solution to the Laplace equation for the potential distribution around a nearly spherical particle.
A Career in Theoretical Physics by P. W. Anderson