A.h. wilson Temperaturen von den klassischen abweichen. Die Ursache dieser Entartung is in einer Quantelung der Molekularbewegungen zu suchen Bei allen Theorien der Entartung werden immer mehr oder weniger willkiirliche Annahmen uber das statistische Verhalten der Molekule, oder uber ihre Quante- ng gemacht. In der vorliegenden Arbeit wird nur die von Pauli zuerst ausges- prochene. Annahme benuzt, dass in einem System nie zwei gleichwertige Elemente vorkommen konnen, deren Quantenzahlen vollstandig ubereinstim men. Mit dieser Hypothese werden die Zustandsgleichung und die innere Energie des idealen Gases abgeleitet; der Entropiewert fur grosse Temperaturen stimmt mit der Stern-Tetrodeschen uiberein In addition to assuming the Pauli principle, Fermi used the old quantum theory to determine the allowed energy levels of the individual atoms by supposing that they behaved like harmonic oscillators with quantum numbers 1, 82, 83(8=0, 1, 2, . )and energies hvs, with 8=81+82+83 Then, if the total number of atoms is N and the total energy is Ehv,∑N=N,∑8N= where N, is the number of atoms with quantum numbers 8. The number of com plexions for given 8 is Q=(8+1)(s+2)N, and the number of arrangements of the N, atoms over the @, levels complying with the Pauli principle is W=QV/IN1(Q,-N)1 Hence, maximizing W, subject to the conditions(1), we have N=Q This is the first appearance of the Fermi function, but, though the derivation is correct according to the assumptions made, Fermi (or Pauli)statistics is inapplic- able to structureless monatomic gases(i.e gases whose atoms haveno uncompensated electronic or nuclear spin). The same error was made by P. A. M. Dirac later in I926 in his paperOn the theory of quantum mechanics, and perhaps with less justifi cation. Fermi based his arguments on the old quantum the eory, whereas Dirac wrote in the context of the new quantum theory. Starting from the consideration that the Hamiltonian of a system of indistinguishable particles is a symmetrical function of the coordinates of the individual particles, Dirac correctly deduced that the wavefunction must be either a symmetrical or an antisymmetrical function of those coordinates To comply with the Pauli principle, symmetrical wavefunctions must be excluded. Dirac wrote, The solution with symmetrical eigenfunctions must be the correct one when applied to light quanta, since it is known that the Einstein Bose statistical mechanics leads to Planck's law of black-body radiation. The solution with antisymmetrical eigenfunctions, though, is probably the correct one for gas molecules, since it is known to be the correct one for electrons in an atom and one would expect molecules to resemble electrons more closely than light40 A. H. Wilson Temperaturen VQn den klaasischen abweichen. Die Ursache die Entartung is in einer Quantelung der M:olekülarbewegungen zu suchen Heg 80n to Bei allen Theorien der Entartung werden immer mehr oder weniger willkürliche Annahmen über das statistische Verhalten der Moleküle, oder über ihre Quan lung gemach ln der vorJi唔enden Arbeìt wird nur die von Pauli zuers .u :es prochene ... Annahme benuz a.s in einem System nie zwei gleichwertige Elemer vorkommen können, deren Quantenzahlen voIl ndig übereinstim men. Mi di erHypo lese werden die Zustandsgleichung und die innere Energie des idealen Gases abgelei也剖; der Entropiewert für gro Temperaturen stimmt der Stern-Tetrodeschen überein ln addition to assuming he Pauli principle, Fermi the old quantum heory to de rmine the a.llowed energy levels of the ìndivìdual atoms by supposing h.t t.hey behaved like harmonìc oscillators with quantum numbers 81, 82, 83 (8‘= 0, 1, 2, ) and energies hV8, with 8 = 81 +82+83 , Then, if he total number of atoms is N and the total energy is Ehv, :E 飞 = N , :E 8N~ = E, (1) where N, ìs the number of ms with quantum numbers 8. The number of m plexiona for given 8 is Q. ~ ,(8+ 1)(8+ 2)N, (2) and the num ber of a. ngements of the atoms over the ~ levels complying with the Pauli principle is 月~ !/[ !(Q -l飞) !] Hence, maximizing r~ subject to the conditiona (川， we have fJ /(1 +ae (3) (4) This is the fi且也 appearance of he Fermi function, but, though the derivation is correct according to the ump ons made, Fermi (or Pauli) 吼叫自tics is inapplic a.ble to 8tructureleωmona阳皿cgaa (i.e ga whose a.tomsha.ve noun mpensa electronic or nuclear spin). The same error made by P. A. M. Dirac la也erin 1926 in hia paper 'On the heory of quantum mechanics', and perhapa wi less justifi￾c. on. Fermi based his arguments on the old quantum heo 巾， where Dirac wrote in he ntext of the new quantum heory. Starting from the conaideration that the Hamiltonian of a. system of indistinguishable pa icles is a. symmetrica.1 function of he ∞。rdinates ofthe individual particles, Dirac correctly deduced h.t the wa.vefunction must be either a symmetrical or an an symmetrica. func创。 of 血。因∞{)rdin也恤s. To comply with he Pa.uli princìple, symmetrical wavefunctions must beexcJ uded. Dira.cwrote, 'Thesolution with symmetrical eigenfunctiona must be he oorrect one when a.pplied to light qua. 恤， sln曲比 is known h.t he Einstein￾Bose statistical mechanÎcs leads to Planck' l a. of bla.ck-body ra.diation. The lution wi antiaymmetrical eigenfunctions ，也hough Îs probably he rrec one for molecules since is known to be the correct one for electrons in a.n atom, and one would expect molecules 阳回回mble electrons more closely than light