A.H. wilson The next major contribution was made by Peierls in 1929 in a paper entitled Zur Theorie der galvanomagnetische Effekte. In order to calculate the electrical conductivity of his model, Bloch had shown that the mean wavevector k of a wave packet was connected with the applied electric field 8 by the relation dk/dt=(-6/), where -e is the electronic charge, and hence that, with v given by(11), the accele ration of an electron due to a field (6, 0, 0)is du,a du, dk,_2pa-edco Commenting on the physical significance of this last equation Peierls stated, Diese Gleichung hat folgende merkwuirdige Konsequenz: Fur k>Ira nimmt mit wachsendem k, der Strom ab, das heisst im Felde wird ein solches Elektron ver- zogert, statt beschleunigt zu werden. Diese Tatsache is so unanschaulich dass es notwendig erscheint ihre Richtigkeit moglichst ohne Vernachlassigungen und Annahmen zu beweisen. Peierls succeeded in this, and he went on to use(13)to explain the existence of anomalous (that is, positive)Hall coefficients. If the conduction electrons were such that the wave numbers k,= k g= ha- ko of the highest filled energy level were less than Ir/a, the Hall coefficient would be negative. If, on the other hand, ko lay in the range(lr/a, m/a), the Hall coefficient would b This discovery gave a rational explanation of the existence of both negative and positive Hall coefficients, and completely cleared up a major mystery, to account for which more than twenty implausible theories had been advanced since 1879 THE PERIOD 1929-33 By the middle of 1929 the state of knowledge was as follows. By making the eroic assumption that the valency electrons in a perfect crystalline solid were not firmly bound, each to a single atom, but had a non-zero chance of jumping to a neighbouring atom, the electrical properties of metals had for the first time been given a rational explanation. The valency electrons could be considered to be quasi-free, and, surprisingly, the energy spectra of quasi-free electrons were such that they could result either in negative(normal) Hall effects or positive(anomalous) Hall effects. However, a number of substantial criticisms could be levelled at the theory. It is sufficient to give two examples In the first place, the problem had only been made tractable by neglecting the electrostatic forces between the valency electrons, except in so far as they could be deemed to give rise to a smeared field having the same symmetry as that due to the atomic nuclei and the core electrons. This meant neglecting the exchange forces between the valency electrons, the dominant effect of which was the basis for the theory of ferromagnetism, first put forward by Heisenberg in 1928 In the second place, while Bloch's theory, as supplemented by Peierls, gave44 A. H. Wilson The next major contribution made by Peierls in 1929 in a. a.阳 entitled 'Zur Theorie der galvanomagnetische tTek 恤'. In order to a. lcul a. te he electrical conductivity of his model, Bloch had shown that he mean wavevecoor k of a. wave packet was nnect‘时 wo the applied electric field 6 by he relation dk/dt - (-./~) (f, (12) where -e he electronic charge, and hence 出盹 wi th v given by (11)，也heac le '"饥 00 of an electroJ1 due a field (1,0, 0) i8 守=技等=-~于eßcosak ( 13) Co mmen川$创】 ng on 也"恤、随 phys刨>0'叫 ifì a. c<。回 of rusl 盹也 equa时也ωion Pe创'"'叶 st ι' D wachs ndem羽、 kι der Strom ab, da.s ei困也 im Felde wird ein solches Elektron ver. zoger毛， sta.tt beschleunig zu werden. Diese Ta.t8ache is 80 una.nscha.uJich a.ss回 notwendig erscheint ihre Rich igk创也 möglichst ohne Vemachlässigungen und Anna.hmen zu bewei n.' Peierls succeeded in this, and he wen也。 se 3) explain the exiatence of anomaloua (that 恼， poaitive) HaU coeffiωents. If出 cond uction elec ons were such h. the wave numbers k1 = k2 - k3 ... ko of highest fill energy level were less than /α，也he HaU coefficient WQuld be negative Iιon the 。由er hand, ko lay in the range (i n: /α π/叫， the Hall coefficient would be positive This dis ery gave a rational explanation of the existence of both negative and positive HaU coeffic ien and completely cle町时 up a major mystery, 10 account for which more h.n wenty implausible ries had been advanced since 1879 THE PERIOD 1929--33 By the middle of 1929 the state of knowledge 翩翩 follows. By making the heroic umption tha.t the valency ec衍。ns in a perfect crysta.lline solid were not firmly bound, each to gle atom, but had a non-zero chance of jumping to a neighbouring 1o ，由 elec~rical propertie8 of metals had for the firs time been given a rational explanation. The valency electrons could be con8idered to be quasi-free, and, surprisingly, the energy spectra of qu i-free electrons were 8uch ha也也 heycould resu either in nega ive(norn Hall effects or positive (anomalous) Hall effects. However, a number of 8ubstantial criticisms could be Jevelled at the theory.1 is uffi ien to give wo example8 1n the fir8t place, t he problem had only been made ractable by neglec ing he electrostatic for 四. be ween the valency electron6, except in 60 far M they could be deemed to give ri to a smeared field havin he 8ame symmetry aa hat due he atomic nuclei and he core electrons. Th.is mean neglecting the exchange forces be he valency electrona ，也 he dominant effect of which was he ba: for he 怕回ry of ferromagnetisffi ，耻，也 put forward by Hei nberg in 1928 Io 回∞nd place, while Bloch's theory. a.s supplemented by Pcie巾， gave