+HLVHQEHUJDQGWKHHDUO\GD\VRITXDQWXPPHFKDQLFV)HOL[%ORFK &LWDWLRQ3K\V7RGD\GRL 9LHZRQOLQHKWWSG[GRLRUJ 9LHZ7DEOHRI&RQWHQWVKWWSZZZSK\VLFVWRGD\RUJUHVRXUFH3+72$'YL 3XEOLVKHGE\WKH$PHULFDQ,QVWLWXWHRI3K\VLFV $GGLWLRQDOUHVRXUFHVIRU3K\VLFV7RGD\+RPHSDJHKWWSZZZSK\VLFVWRGD\RUJ ,QIRUPDWLRQKWWSZZZSK\VLFVWRGD\RUJDERXWBXV 'DLO\(GLWLRQKWWSZZZSK\VLFVWRGD\RUJGDLO\BHGLWLRQ

Downloaded 08 Jan 2013 to 130.113.174.170. Redistribution subject to AIP license or copyright; see http://www.physicstoday.org/about_us/terms

REMINISCENCES OF

Heisenberg and the early daysof quantum mechanicsRecollections of the days, 50 years ago, when a handful of studentsin the "entirely useless" field of physics heard of a strange new mechanicsinvented by Maurice de Broglie, Werner Heisenberg and Erwin Schrodinger.

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 ArnoldSommerfeld'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, run

with firm authority by Debye, might havehad an audience of as much as a couple ofdozenon 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 23Downloaded 08 Jan 2013 to 130.113.174.170. Redistribution subject to AIP license or copyright; see http://www.physicstoday.org/about_us/terms

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 derPhysik. 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-Huckeltheory 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 original Ger-man:

"Gar Manches rechnet Erwin schonMit seiner Wellenfunktion.Nur wissen mocht' man gerne wohlWas 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 Schrodinger

did 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 youdo!"

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 of

his assumption of the electron beingoriginally 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 thelegal 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 almost25 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. Weylhad 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 1976Downloaded 08 Jan 2013 to 130.113.174.170. Redistribution subject to AIP license or copyright; see http://www.physicstoday.org/about_us/terms

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 hissound 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 nothelp much to cheer me up! As soon as Ihad completed the simple formality ofregistering as a student of the Universityin the center of the city I went to thePhysics 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 incharge was Wentzel who, a year later, wasto become Schrodinger's successor inZurich. I did not find him in his officeand was told by an assistant that I couldsee 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 wasreally all right to go up there and knock athis door but I dared to do it anyhow, andalmost from the moment he opened it Irealized that I had come to a new andmuch warmer academic climate. Used tothe great distance that separated thestudents 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 italmost difficult for me to address himwith the normal "Herr Professor" butvery easy to show him a little paper I hadwritten before I came to Leipzig.

My paper had been motivated bySchrodinger's old dislike of electronwavepackets' disagreeable habit ofspreading, and I had had the naive ideathat they might be cured from it at leastpartially by radiation damping. To try itout, I had done a serious calculation forthe 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; hesaid I should ask Heisenberg, who wasexpected in a few days.My first paper

Although his great achievements datedback no more than about two years,Heisenberg was already very famous asthe 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 Ilost 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, ithad 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 towork them out for the general case. Withthe help of P. A. M. Dirac's paper on ra-diation effects and a few more tricks, Imanaged to do that rather quickly, con-firming Heisenberg's prediction, and itbecame my first published paper. It ap-peared in the Physikalische Zeitschrift asa precursor to the well known paper ofVictor 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 Iwent back to Leipzig after New Year Iproposed 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 25Downloaded 08 Jan 2013 to 130.113.174.170. Redistribution subject to AIP license or copyright; see http://www.physicstoday.org/about_us/terms

SCHRODINGER

down to earth such as, for example, fer-romagnetism or the conductivity of met-als.

As to ferromagnetism, he thought thatit had to be explained by an exchange in-tegral between electrons, with the oppo-site sign from that in helium so as to favora parallel rather than opposite orientationof their spins. He had shown before thatthe difference between the ortho and parastates of the helium atom were due to thedependence of the exchange energy ontheir symmetry properties and had alsorecognized that the analogous phenome-non for the protons in the hydrogen mol-ecule led to the two forms, ortho and para,of hydrogen. Well, his idea sounded soconvincing that I felt there was no pointof my going into it. It was obvious to methat Heisenberg already knew the essen-tials; indeed,.he soon wrote the paper onthe subject that laid the groundwork forthe modern theory of ferromagnetism. Itwas not until two years later that I some-what embellished his treatment by theintroduction of spinwaves.Electrons in crystals

There was a greater challenge in hisother suggestion, to do something moreabout the properties of metals. Goingbeyond the earlier work of Paul Drudeand H. A. Lorentz, Wolfgang Pauli hadalready given a first new impetus to thefield by invoking Fermi statistics to ex-plain the temperature-independent par-amagnetism of conduction electrons;Sommerfeld had gone further by dis-cussing the consequences for the specificheat and the relation between the thermaland the electric conductivity of metals.Both, however, had treated the conduc-tion electrons as an ideal gas of free elec-trons, which didn't appear in the leastplausible to me.

When I started to think about it, I feltthat the main problem was to explain howthe electrons could sneak by all the ions

in a metal so as to avoid a mean free pathof the order of atomic distances. Such adistance was much too short to explainthe observed resistances, which even de-manded that the mean free path becomelonger and longer with decreasing tem-perature. But Heitler and London hadalready shown-how electrons could jumpbetween two atoms in a molecule to forma covalent bond, and the main differencebetween a molecule and a crystal was onlythat there were many more atoms in aperiodic arrangement. To make my lifeeasy, I began by considering wavefunc-tions in a one-dimensional periodic po-tential. By straight Fourier analysis Ifound to my delight that the wave differedfrom the plane wave of free electrons onlyby a periodic modulation.

This was so simple that I didn't thinkit could be much of a discovery, but whenI showed it to Heisenberg he said rightaway: "That's it!" Well, that wasn'tquite it yet, and my calculations were onlycompleted in the summer when I wrotemy thesis on "The Quantum Mechanicsof Electrons in Crystal Lattices."

I then left Leipzig to become for a yearthe assistant of Pauli in Zurich and tospend another year as Lorentz Fellow inHolland. It was not until the fall of 1930that I returned to Leipzig, this time asHeisenberg's assistant, and by then theearly days of quantum mechanics werereally over, although many of its impor-tant consequences were yet to comeandare still coming.

I don't think many of us realized thatwe had just gone through quite a uniqueera; we thought that this was just the wayphysics was normally to be done and only

wondered why clever people had not seenthat earlier. Almost any problem thathad been tossed around years before couldnow be reopened and made amenable toa consistent treatment. To be sure, therewere a few minor difficulties left, such asthe infinite self-energy of the electron andthe question of how it could exist in thenucleus before beta decay; and nobodyhad yet derived the numerical value of thefine-structure constant. But we weresure that the solutions were just aroundthe corner and that any new ideas thatmight be called for in the process would beeasily supplied in the unlikely event thatthis should be necessary. Well, the lastfifty years have taught us at least to be alittle more modest in our expectations.Heisenberg the teacher and scientist

From what I have told about the yearwhen I had the good fortune to beHeisenberg's first student it may alreadybe evident that he stands in the center ofmy memories of this most formative pe-riod in my life as a physicist. It is not onlythat he suggested the theme of my thesis,but I owe it to him that I caught the realspirit of research and that I dared to takethe first steps in learning how to walk. IfI should single out one of his great quali-ties as a teacher, it would be his im-mensely positive attitude towards anyprogress and the encouragement hethereby conferred.

This does not mean that one alwaysreceived praise from him and that, onoccasions, he could not be quite severe.Once during my thesis work I becamestuck on a rather awkward difficulty andhoped that he would help me out. But

WENTZEL

26 PHYSICS TODAY / DECEMBER 1976Downloaded 08 Jan 2013 to 130.113.174.170. Redistribution subject to AIP license or copyright; see http://www.physicstoday.org/about_us/terms

PAULI

after I had explained it to him he onlysaid: "Now that you have analyzed thesource of the trouble it can't be all thathard to see what to do about it."

Of course, I felt rather depressed, butjust to get out of it I pushed once moreand in some cumbersome way finallymanaged indeed to get over the obstacle.It was not the mathematical method butonly physical content that ever matteredto Heisenberg. As to elegance he mighthave agreed with Ludwig Boltzmann'sopinion that it was "best left to tailors andbootmakers."

Besides my year as Heisenberg's stu-dent, I spent the two more years, 1930-31and 1932-33, in Leipzig until Hitler suc-ceeded in forming a new Germany in hisown frightful image. What followed istoo well known for me to dwell upon, butI cannot refrain from one sad comment onhuman nature. The very devotion totheir work and their detachment from thedark irrational passions spreading aroundthem caught most of even the finest Ger-man scientists unprepared for the on-coming flood. Those who did not leavewere with few exceptions swept along andwere left, each in his own way, to strugglewith their inner conflicts.

But my memories of Heisenberg belongto the happier time before those events.Many of them relate to entirely informaland anything-but-professional conver-sations on walks, in his ski hut in the Ba-varian Alps or under other relaxed cir-cumstances. These remain no less pre-cious to me than our talks on physics, andI want to tell in conclusion about two ofthem that I remember most vividly.

Once I came back after dinner to myroom in the Institute to finish some work.While I sat at my desk I heard Heisen-berg, who was an excellent pianist, playingin his apartment under the roof of the

building. It was already late at nightwhen he came down to my room and saidhe just wanted to talk a little before goingto bed after he had practiced a few bars ofa Schumann concerto for three hours.And then he told me that Franz Liszt,when he was already a famous pianist,found that his scales of thirds and fifthswere not smooth enough. So he cancelledall engagements, and for a year practicednothing but these scales before he startedto perform again. The reason I remem-ber this so well is that I felt that Heisen-berg, without intention, had told mesomething important about himself. Theaudience of Liszt after that year musthave thought it a wonder how easily hewas able to play those difficult scales.But the real wonder was of course that hehad had the strength and the gift of con-centration to keep on perfecting themincessantly for a whole year.

Now, one of the most marvellous traitsof Heisenberg was the almost infallibleintuition that he showed in his approachto a problem of physics and the pheno-mental way in which the solutions cameto him as if out of the blue sky. I haveasked myself whether that wasn't a formof the "Liszt phenomenon," and for thatthe more admirable. Not that Heisen-berg would ever have cancelled all otheractivity for a year to master a specialtechnique. But we all knew the dreamyexpression on his face, even in his com-plete attention to other matters and in hisfullest enjoyment of jokes or play, whichindicated that in the inner recesses of thebrain he continued his all-importantthoughts on physics.

There is another remark he once madethat I consider even more characteristic.We were on a walk and somehow began totalk about space. I had just read Weyl'sbook Space, Time and Matter, and underits influence was proud to declare thatspace was simply the field of linear oper-ations.

"Nonsense," said Heisenberg, "space isblue and birds fly through it."

This may sound naive, but I knew himwell enough by that time to fully under-stand the rebuke. What he meant wasthat it was dangerous for a physicist todescribe Nature in terms of idealized ab-stractions too far removed from the evi-dence of actual observation. In fact, itwas just by avoiding this danger in theprevious description of atomic phenom-ena that he was able to arrive at his greatcreation of quantum mechanics. In cel-ebrating the fiftieth anniversary of thisachievement, we are vastly indebted tothe men who brought it about: not onlyfor having provided us with a most pow-erful tool but also, and even more signif-icant, for a deeper insight into our con-ception of reality.

* * *This article is an adaptation of a talk given 26April 1976 at the Washington, DC meeting ofThe American Physical Society.

High Pressure

Tem-PresReactorVessels

to 60,000 psi 900CTem-Pres designs and constructs reactor

vessels that accept simultaneous temperatures andpressures far beyond the limits of standard com-mercial units. Constructed of Rene 41, 316stainless steel and Unitemp L-605. these vesselsmeet the needs of both academic and industriallaboratories for elevated pressure and temperaturestudies.

P-V-T studies Accelerated Corrosion Testing Special Environmental Testing Solubility Determinations Electrical Conductivity Measurements Syntheses at Elevated Temperatures

and Pressures Stability and Phase Compatibility

Determinations High Pressure Differential Thermal

Analyses H Crystal Growth in Neutral or Pressure

Media

specialists in high pressure/high temperatureresearch systems

contact R. M ShoffLeco CorporationTem-Pres Division1401 South Atherton StreetState College, Pennsylvania 16801Phone. 814-237-7631

LECOCircle No. 23 on Reader Service CardPHYSICS TODAY / DECEMBER 1976 2 7

Downloaded 08 Jan 2013 to 130.113.174.170. Redistribution subject to AIP license or copyright; see http://www.physicstoday.org/about_us/terms