-
+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