Heisenberg and the Early Days of Quantum Mechanics, Felix Bloch, Physics Today 1976

Felix Bloch describes the intriguing intellectual history behind the development of the revolutionary field of quantum mechanics. Bloch was a student when Heisenberg, Schrodinger and others were first grappling with the subject.
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Felix  Bloch It is appropriate in this year, when wecelebrate the 50th anniversary of quan-tum mechanics, and during which  we  havebeen saddened by the death of one of itsleading founders, Werner Heisenberg, toreminisce about the formative years of thenew mechanics. At the time when thefoundations of physics were being re-placed with totally new concepts I was astudent of physics. I sat in the collo-quium audience when Peter Debye madethe suggestions to Erwin Schrodinger thatstarted him on the study of de Brogliewaves and the search for their waveequation. It was from Heisenberg, as hisfirst doctorate student, that I caught thespirit of research, and that I received theencouragement to make my own contri-butions. First inklings Let me begin by going back to 1924,when I entered the Swiss Federal Insti-tute of Technology in my home town ofZurich. I began as a student of engi-neering but after a year and good deal ofsoul searching I decided, against all goodsense, to switch over to the entirely use- less  field of physics. The E. T. H., as itis known from its German name, was aninstitution of great international reputeand in my newly chosen field of studies Ihad heard of such famous men as PeterDebye and Hermann Weyl. In fact, thefirst introductory course of physics I tookwas taught by Debye and, without know-ing much about his scientific work, I re-alized from the high quality of  his  lecturesat the Institute that here was a greatmaster of his field.There was a good deal less to be en-thusiastic about in the other courses one Felix Bloch, winner (with E. M.  Purcell of the1952 Nobel Prize in physics, is professoremeritus of physics at Stanford University. could take, and there was nothing like thecomplete menu that is presented to thestudents nowadays. Once in a while, aprofessor would offer a special course ona subject he just happened to be inter-ested in, completely disregarding thetremendous gaps in our knowledge left bythis system. Anyway, there was only ahandful of us foolish enough to studyphysics and it was evidently not thoughtworthwhile to bother much about these odd fellows. The only thing we coulddo about it was to go to the library andread some books, although nobody wouldadvise us which ones to choose.Among the first I hit upon was Arnold Sommerfeld s  Atomic Structure andSpectral Lines,  which I found fascinating;the only trouble was that I could not un-derstand most of it because I knew far toolittle of mechanics and electrodynamics.So at first I had to learn about thesesubjects from other books, to truly ap-preciate what Sommerfeld said; but thenit conveyed the good feeling that every-thing about atoms was completely knownand understood. The fact that one reallycould handle only periodic systems andonly those that allowed a separation ofvariables did not seem a great cause forconcern. Therefore, when I saw a paperin which somebody tried to squeeze thetheory of the Compton Effect into thatscheme, I was more impressed than dis-couraged by the complicated mathematicsspent in the effort.The news that the foundations of  a  newmechanics had already been laid byMaurice de Broglie and Heisenberg hadhardly leaked to Zurich yet and certainlyhad not penetrated to our lower strata.The first inklings of such a thing came tome in early  1926;  I had by then started toattend the physics colloquium regularly,although most of what I heard there wasfar above my head. The colloquium, runwith firm authority by Debye, might havehad an audience of  as  much as a couple of dozen—on  a good day.Physics was also taught at the Univer-sity of Zurich by a smaller and rather lessillustrious faculty than that at the E. T. H.Theory there was in the hands of  a  certainAustrian of  the  name of Schrodinger, andthe colloquium was alternately held atboth institutions. I apologize to myfriends who already have heard from mewhat I am going to tell you now. My ac-count may not conform to the stricteststandards of history, which accord valid-ity only to written documents, nor will Ibe able to render the exact words I heardon those occasions, but I can vouchsafethat, in content, I shall report the truthand only the truth. A wave equation is found Once at the end of  a  colloquium I heardDebye saying something like: Schro-dinger, you are not working right now onvery important problems anyway. Whydon't you tell us some time about thatthesis of de Broglie, which seems to haveattracted some attention. So,  in one of the next colloquia, Schro-dinger gave a beautifully clear account ofhow de Broglie associated a wave with aparticle and how he could obtain thequantization rules of Niels Bohr andSommerfeld by demanding that an inte-ger number of waves should be fittedalong a stationary orbit. When he hadfinished, Debye casually remarked that hethought this way of talking was ratherchildish. As a student of Sommerfeld hehad learned that, to deal properly withwaves, one had to have a wave equation.It sounded quite trivial and did not seemto make a great impression, but Schro-dinger evidently thought a bit more aboutthe idea afterwards.Just a few weeks later he gave another PHYSICS TODAY / DECEMBER 1976 23 Downloaded 08 Jan 2013 to Redistribution subject to AIP license or copyright; see  HEISENBERG talk in the colloquium which he started bysaying: My colleague Debye suggestedthat one should have a wave equation;well, I have found one And then he told us essentially what hewas about to publish under the title Quantization as Eigenvalue Problem asa first paper of  a  series in the  Annalen  der Physik.  I was still too green to reallyappreciate the significance of this talk,but from the general reaction of the au-dience I realized that something ratherimportant had happened, and I need nottell you what the name of Schrodinger hasmeant from then on. Many years later,I reminded Debye of  his  remark about thewave equation; interestingly enough heclaimed that he had forgotten about it andI am not quite sure whether this was notthe subconscious suppression of his regretthat he had not done it  himself.  In anyevent, he turned to me with a broad smileand said: Well, wasn't I right? Of course, there was afterwards a lot oftalk among the physicists of Zurich, in-cluding even the students, about thatmysterious psi of Schrodinger. In thesummer of 1926, a fine little conferencewas held there and at the end everyonejoined a boat trip to dinner in a restauranton the lake. As a young  Prwatdozent, Erich  Hiickel  worked at that time on whatis now well known as the  Debye-Huckel theory of strong electrolytes, and on theoccasion he incited and helped us tocompose some verses, which did not showtoo much respect for the great professors. As  an example, I want to quote the one onErwin Schrodinger in its srcinal Ger-man:  Gar  Manches rechnet Erwin  schon Mit seiner Wellenfunktion. Nur wissen  mocht'  man gerne  wohl Was man  sich  dabei vorstell'n  soil. In free translation:Erwin with his psi can doCalculations quite a few.But one thing has not been seen:Just what does psi really mean?Well, the trouble was that Schrodingerdid not know it  himself.  Max Born's in-terpretation as probability amplitudecame only later and, along with no less acompany than Max Planck, Albert Ein-stein and de Broglie, he remained skep-tical about it to the end of his life. Muchlater, I was once in a seminar wheresomeone drew certain quite extendedconclusions from the Schrodinger equa-tion, and Schrodinger expressed his gravedoubts that it could be taken that seri-ously; whereupon Gregor Wentzel, whowas also there, said to him: Schrodinger,it is most fortunate that other people be-lieve more in your equation than you do Schrodinger thought for a time that awave packet would represent the actualshape of an electron, but it naturallybothered him that the thing had a ten-dency to spread out in time as if the elec-tron would gradually get fatter and fat-ter.As I said before, I was too green then tounderstand these things and still strug-gled with the older theories. In readingDebye's paper of 1923 on the Comptoneffect, it occurred to me that, instead ofhis assumption of the electron beingsrcinally at rest, one should take intoaccount its motion on a stationary orbit inthe atom. I thought this was such a goodidea that I even had the incredible cour-age to go to Debye's office and tell it tohim. It really wasn't all that wrong but heonly said: That's no way any more totalk about atoms; you better  go  and studySchrodinger's new wave mechanics. Well, you would not disobey the au-thorities and, of course, he was again quiteright. So this is what I did; Schrodinger'snext papers on wave mechanics appearedshortly, one after the other. I did notlearn about the matrix formulation ofquantum mechanics by Heisenberg, Bornand Pascual Jordan until I read thatpaper of Schrodinger's in which heshowed the two formulations to lead tothe same results. It did not take me toolong to absorb these new methods, and Iwish I could confer to the younger physi-cists who read this article the marvellousfeeling we students experienced at thattime in the sudden tremendous wideningof our horizon. Since we were not bur-dened with much previous knowledge, theprocess was quite painless for us, and wewere blissfully unaware of the deepunderlying change of fundamental con-cepts that the more experienced olderphysicists had to struggle with.Although I had already begun an ex-periment in spectroscopy, I was now en-tirely captured by theory and I felt the legal  entrance into the guild to be con-firmed through my acquaintance withWalter Heitler and Fritz London. Theyhad just obtained their PhD's and hadcome to Schrodinger's Institute, wheretogether they worked on their theory ofcovalent bonds. I must have met them ina seminar, and it was a great thing for methat they asked me to join them in someof their walks through the forests aroundZurich. For us students the professorslived somewhere in the clouds, and thattwo real theorists at the ripe age of almost 25  should even bother about a greenhornlike me was ample cause for my gratitudeto them. Leipzig This great period in Zurich came to asudden end in the fall of  1927  when someof the most important men there simul-taneously succumbed to the pull of thelarge magnet in the North, represented bythe flourishing science in Germany.  Weyl had accepted a position in Gottingen,Schrodinger in Berlin and Debye inLeipzig, and it was clear to me that I hadto join the exodus if I did not want mytime as a student to drag on much longer.The question was only where to  go;  I wastempted to follow either London's ex-ample and  go  with Schrodinger to Berlin,or Heitler's, and go to Gottingen.Before deciding, however, I went to askDebye for his opinion, and he advised meto do neither but instead to come to 24 PHYSICS TODAY / DECEMBER 1976 Downloaded 08 Jan 2013 to Redistribution subject to AIP license or copyright; see  Leipzig. There  I  would work withHeisenberg whom he, as the new directorof the Institute of Physics of the Univer-sity, had persuaded to accept the profes-sorship for theoretical physics. Debye'spower of persuasion was quite formidableand I could not resist it either, particularlybecause  I had  previous evidence  of his sound judgment. So,  in  October 1927 before  the  begin-ning of the winter semester,  I  left my nicehome town for the first time, to arrive ona cold gray morning  in  that rather uglycity  of  Leipzig. The little room  I  foundfor rent from  a  family overlooked  a  rail-road yard;  the  noise  and  smoke  did not help much  to  cheer me  up As soon as  I had completed  the  simple formality  of registering as a student of the Universityin  the  center  of the  city  I  went  to the Physics Institute, which was located nearthe outskirts.It was an old building opposite  a  cem-etery  on  one side and adjoining the gardenof a mental institution on the other, butoccupied  by  people who were  far  frombeing either dead  or  crazy. Heisenberghad  not  arrived  yet and the  theorist  in charge was Wentzel who, a year later, wasto become Schrodinger's successor  in Zurich.  I did not  find him  in  his officeand was told by an assistant that  I  could see  him in his apartment on the third floorof the building.It was quite customary at that time forprofessors to have official living quartersin  or  adjacent  to  their institutes; Debyehad the Director's villa in a side wing, andfor young bachelors like Wentzel and alsoHeisenberg upon  his  arrival there weresmall but comfortable apartments underthe  roof. I  was not at all  sure whether  it was really all right to  go  up there and knock athis door but I dared to do  it  anyhow, andalmost from  the  moment  he  opened  it I realized that  I had  come  to a  new  and much warmer academic climate. Used  to the great distance that separated  the students and professors in freedom-lovingSwitzerland,  I  had expected the prover-bial discipline of the Germans  to  call foran even stricter caste system. Instead,Wentzel received  me  with  the  informalcordiality  of a  colleague, which made  it almost difficult  for me to  address  him with  the  normal  Herr Professor but very easy to show him a little paper I hadwritten before  I  came to Leipzig.My paper  had  been motivated  by Schrodinger's  old  dislike  of  electronwavepackets' disagreeable habit  of spreading,  and I  had had the naive ideathat they might be cured from  it at  leastpartially by radiation damping. To try  it out,  I  had done  a  serious calculation  for the harmonic oscillator, with  the  resultthat  a  suitable gaussian wavepacket,without spreading, would perform a nicedamped oscillation that  led  asymptoti-cally  to the  wavefunction  of  the groundstate. Wentzel made some kind com- DEBYE ments  but modestly disclaimed sufficientexpert knowledge  to  pass judgment;  he said  I  should  ask  Heisenberg, who  was expected in  a  few days. My first paper Although his great achievements datedback  no  more than about  two  years,Heisenberg was already very famous  as the founder of the new form of mechanics,which accounted for quantum phenome-na by abandoning such fundamental ideasas motion in an orbit and replacing themby concepts referring  to the  actual  ob- servation  of  atomic processes.  I  think  I lost  my  breath  for a  moment whenWentzel introduced  me to  this greatphysicist in the person of  a  slender youngman. Maybe Debye  had  already men-tioned to him that he knew me from Zur-ich; in any case, as soon as he shook handsand started  to  talk  to me in his  simplenatural way,  I  had the feeling that  I  was accepted. Just as with Wentzel, there was no in-dication whatever of  a  barrier to separateus on the grounds of Heisenberg's vastlysuperior standing,  and  this was  the ex- perience  I had  with many  of the  otherprominent scientists  I  later met  in  Ger-many. While  it  surprised me  at  first,  it had quite  a  simple reason: These menwere so entirely devoted to their scienceand their work spoke so clearly  for  itselfthat there  was  really no room or reason forany pretense,  be it in the  form  of  grandmanners  or of  false modesty. WithHeisenberg there was the additional fac-tor of his youth; as  a  professor at the ageof  26  he was only about four years older,although in the time scale of theorists thisalready put him something like two gen-erations ahead of me.As to my hopes for keeping wavepack-ets together  by  radiation damping, he onlysmiled and said that, if anything,  it  couldof course only make them spread evenmore. Nevertheless he thought my cal-culations on the harmonic oscillator werea good start, and that  I  should go  on to work them out for the general case. Withthe help of  P.  A. M. Dirac's paper on ra-diation effects  and a few  more tricks,  I managed  to  do that rather quickly, con-firming Heisenberg's prediction,  and it became my first published paper.  It  ap- peared in  the  Physikalische Zeitschrift  asa precursor  to the  well known paper  of Victor Weisskopf and Eugene Wigner onradiation damping  and  natural linewidths.Before  the  Christmas vacations,Heisenberg said that I should think abouta topic for my doctor's thesis: This I didmostly while skiing  in  Switzerland  afterI had gone home.  I  knew the importanceof Paul Ehrenfest's adiabatic theorem inthe older quantum theory,  and  when  I went back  to  Leipzig after New Year  I proposed  for  my thesis its reformulationin quantum mechanics. Yes,  said Heisenberg, one might dothat, but I think you had better leave suchthings  to  the learned gentlemen  of  Got-tingen. What he meant was the school of Born,which  had the  reputation  of  being  par- ticularly skilled  in and  rather fond  of elaborate mathematical formalisms.Instead,  he  suggested something more PHYSICS TODAY   DECEMBER  1976 25 Downloaded 08 Jan 2013 to Redistribution subject to AIP license or copyright; see
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