Maker Pro
Maker Pro

Tunneling

B

Baron

Jan 1, 1970
0
George Herold Inscribed thus:
Really? Do I need a small contact area? (etched Nickel wire?)
Are there no oxides involved?
Are there magnetic field effects? (that could be cool.)
(I've always wanted a piece of Nickel.)

Some of the electrodes in tubes and crt's are made from nickel.
 
G

George Herold

Jan 1, 1970
0
That's my whole point! You are not counting photons, you're counting
ionization events which occur with a probability proportional to the
local EM power. At very low intensities, the interference pattern is
there, but it will cause detection events only occasionally. If you
really want to have photons, reserve the word for the amount of energy
that is exchanged between the field and a particle. At least that's
local and essentially instantaneous, doing away with all these
non-locality problems.




Is it really so mysterious that the EM waves created by parametric
down conversion have certain collectively conserved quantities?
A BBO crystal is basically an array of tiny non-linear harmonic-
injection-locked resonators. No need to think in terms of photons
to explain its operation.

Jeroen Belleman- Hide quoted text -

- Show quoted text -

Yeah sure, I'm basically agnostic on whether photons are 'real'.
(It doesn't matter to me one way or other.)
To me they are as real as lattice vibration phonons*.
I don't totally understand either, but it's a darn useful concept for
thinking about things (and getting the right answer).

George H.


*or all the other 'nons in solid state phyiscs.
 
M

Mr Stonebeach

Jan 1, 1970
0
What experiment would demonstrate unequivocally that
light itself is conveyed by discrete photons?

What about squeezed states of light? If your transmitter
sends eg. a photon-bunched state, rather than the coherent
state, and you notice at the receivcer end that your counting
statistics change - shouldn't the field somehow carry
information about what statistics the transmitter uses?

Regards,
Mikko
 
M

Mr Stonebeach

Jan 1, 1970
0
Hi Jeroen,

I don't want to argue, but rather try to understand.
You have obviously put some thought on the
light-matter interaction puzzles. However, as much
as I dislike the whizzing-ball picture of photons, I'm
wondering whether it is possible to discard the photon
concept (in the sense used by eg. Louisell, or Glauber)
in as radical a way as you seem to suggest.

For example, in superconducting transition edge
sensors the smallest excitation is *much* smaller
than the energy of absorbed photons. Then it must
be some other mechanism than the physics of the
*detector* which forces the EM energy being
absorbed in the lumps of the size omega hbar.

An example is the work of Aaron Miller et al
http://people.bu.edu/alexserg/APL_2003.pdf
From the detector physics point-of-view, they
*would be* capable to see two 0.4eV events, or
three 0.27eV events when shining a 1.55um laser
on the detector - but they never see those, only
single 0.8eV events. Or, more accurately: they
see the Poisson distribution, characteristic
of a coherent state being received.

Now, assume that a detector with a different
composition (say, an APD - although I don't
know offhand if they have sufficient energy resolution)
is detecting the same phenomenon. If it, too, sees
only single 0.8eV events and not any double
0.4eV events, wouldn't it be more natural
to ascribe the 'lumpedness' as a property of
the EM field rather than the property of the detector?

In particular, if you shorten the wavelength of the
illuminating laser (i.e. change something in the
transmitter side), you see that the size of absorbed
energy lumps goes up. Now, detector physics (including
the detectors excitation spectrum) supposedly does
not change, still the lump size it sees changes.
Wouldn't it in this case be more natural to associate
the lump size to either the transmitter or the EM field,
rather than to the detector? (OK, I suppose you can
answer 'it is the transmitter', but then a similar argument
about a transmitter of any physical composition
can be constructed).

I do agree that the photon absorption phenomena *could*
be explained by a postulated physical phenomenon which
always occurs at the light-matter interaction, and which
always gives the lump size of hbar-omega regardless
of the detector physics (solid state, gas ...) and regardless
of the range of energy excitations available in the detector
(semiconductor gap, superconducting gap, continuous
spectrum of thermal excitations...). But isn't such a
postulate much more awkward than accepting the
discreteness to be a feature of the EM field itself (in
the Louisell sense)?
Yes, of course they exist. What they detect are not photons in the
sense of light particles, but discrete charges, electrons, dislodged
from the matter they are made of by the incident light waves. This
occurs with a probability proportional to the power density of the
local EM wave, provided its frequency is above a certain threshold,
characteristic of the detector material. This is by no means
proof that light itself is conveyed in discrete packets.

There exists no source of countable single photons at precisely
defined instants. All they do is to attenuate the light of a
picosecond laser by a sufficient amount to make the detector
produce one or fewer events per laser pulse on average. An APD
has huge gain. A sizable output pulse results from a single
electron-hole pair. The event rate has Poisson statistics,
convolved by the laser pulse shape.

Jeroen Belleman

I think single-photon sources *do* exist, but I better not
make that claim too strongly before refreshing my memory
on the subject. There has been a review, I must dig it out...

At least: non-poissonian photon sources *do* exist (e.g
bunched or anti-bunched); whether there are externally
triggerable ones nowadays I'm not sure.

I remember being intriguiged in late-90's by claims that
an ordinary LED, when driven by sub-poissonian current,
would act effectively as single photon emitter. The question
is of course how to create that sub-poissonian current,
in particular when there is the junction capacitance present.
I should dig out those old papers as well...

Regards,
Mikko
 
M

Mr Stonebeach

Jan 1, 1970
0
Is it really so mysterious that the EM waves created by parametric
down conversion have certain collectively conserved quantities?
A BBO crystal is basically an array of tiny non-linear harmonic-
injection-locked resonators. No need to think in terms of photons
to explain its operation.

Jeroen Belleman

Does this 'conserved quantity' way of thinking really
work if one puts it to a closer scrutiny? To me it sounds
like you're giving the classical EM field the role of
'hidden variables' in the Bell sense.

I mean, saying that "the EM field propagates as wave
but is absorbed in a discrete way" *does* resembles the
QM description where wave function propagates in an
unitary manner but collapses at the measurement.
Still, the connection must be made in a more clever
way IMO than just kind of stating that the classical EM
field somehow *is* the wave function.

In the standard prescription one must replace the field
variables E, B by field operators, and all the standard
QFT yada yada - *then* you can account for all the
nonclassical experimentally verified phenomena such
as GHZ states, but thereby also the concept of photon
creeps in, in the form of the discrete excitations of the
harmonic oscillator. And this is a part of the EM field,
not a part of the detector or the transmitter physics.

Regards,
Mikko
 
J

Jeroen Belleman

Jan 1, 1970
0
Hi Jeroen,

I don't want to argue, but rather try to understand.
You have obviously put some thought on the
light-matter interaction puzzles. However, as much
as I dislike the whizzing-ball picture of photons, I'm
wondering whether it is possible to discard the photon
concept (in the sense used by eg. Louisell, or Glauber)
in as radical a way as you seem to suggest.

For example, in superconducting transition edge
sensors the smallest excitation is *much* smaller
than the energy of absorbed photons. Then it must
be some other mechanism than the physics of the
*detector* which forces the EM energy being
absorbed in the lumps of the size omega hbar.

An example is the work of Aaron Miller et al
http://people.bu.edu/alexserg/APL_2003.pdf
From the detector physics point-of-view, they
*would be* capable to see two 0.4eV events, or
three 0.27eV events when shining a 1.55um laser
on the detector - but they never see those, only
single 0.8eV events. Or, more accurately: they
see the Poisson distribution, characteristic
of a coherent state being received.

Now, assume that a detector with a different
composition (say, an APD - although I don't
know offhand if they have sufficient energy resolution)
is detecting the same phenomenon. If it, too, sees
only single 0.8eV events and not any double
0.4eV events, wouldn't it be more natural
to ascribe the 'lumpedness' as a property of
the EM field rather than the property of the detector?

In particular, if you shorten the wavelength of the
illuminating laser (i.e. change something in the
transmitter side), you see that the size of absorbed
energy lumps goes up. Now, detector physics (including
the detectors excitation spectrum) supposedly does
not change, still the lump size it sees changes.
Wouldn't it in this case be more natural to associate
the lump size to either the transmitter or the EM field,
rather than to the detector? (OK, I suppose you can
answer 'it is the transmitter', but then a similar argument
about a transmitter of any physical composition
can be constructed).

I do agree that the photon absorption phenomena *could*
be explained by a postulated physical phenomenon which
always occurs at the light-matter interaction, and which
always gives the lump size of hbar-omega regardless
of the detector physics (solid state, gas ...) and regardless
of the range of energy excitations available in the detector
(semiconductor gap, superconducting gap, continuous
spectrum of thermal excitations...). But isn't such a
postulate much more awkward than accepting the
discreteness to be a feature of the EM field itself (in
the Louisell sense)?


I think single-photon sources *do* exist, but I better not
make that claim too strongly before refreshing my memory
on the subject. There has been a review, I must dig it out...

At least: non-poissonian photon sources *do* exist (e.g
bunched or anti-bunched); whether there are externally
triggerable ones nowadays I'm not sure.

I remember being intriguiged in late-90's by claims that
an ordinary LED, when driven by sub-poissonian current,
would act effectively as single photon emitter. The question
is of course how to create that sub-poissonian current,
in particular when there is the junction capacitance present.
I should dig out those old papers as well...

Regards,
Mikko
Hi Mikko,

Thank you for your comments. APDs have no energy resolution and
no ability to distinguish multi-photon events worth mentioning.
I wasn't aware of Aaron Miller's work, but it looks closely
related to the photo-electric effect, for which a semi-classical
analysis appears to work. It's much better that the photo-electric
effect in the sense that there is no energy lost to the work
function.

Regards,
Jeroen Belleman
 
M

Mr Stonebeach

Jan 1, 1970
0
Hi Mikko,

Thank you for your comments. APDs have no energy resolution and
no ability to distinguish multi-photon events worth mentioning.
I wasn't aware of Aaron Miller's work, but it looks closely
related to the photo-electric effect, for which a semi-classical
analysis appears to work. It's much better that the photo-electric
effect in the sense that there is no energy lost to the work
function.

Regards,
Jeroen Belleman

Hi Jeroen,

Let me still add the link to the photon source review I had
in mind: http://dx.doi.org/10.1063/1.3610677 .

I only found one LED emitter reference (from a seminar talk I
gave as a grad student in -97 about QND measurements):
http://dx.doi.org/10.1103/PhysRevLett.71.2006
but that is not the one I'm thinking - authors were japanese
in that paper.

Regards,
Mikko
 
M

Mr Stonebeach

Jan 1, 1970
0
  I only found one LED emitter reference (from a seminar talk I
gave as a grad student in -97 about QND measurements):http://dx.doi.org/10.1103/PhysRevLett.71.2006
but that is not the one I'm thinking - authors were japanese
in that paper.

Found it, it's the ref. 5 in the Roch-Poizat-Grangier paper:
http://dx.doi.org/10.1209/0295-5075/4/3/007 (and the authors
are not japanese - I must have been thinking Yamamoto's work).

The experiment looks even more fishy (wonderful) than I
remebered. Although the effect they see is small.

Regards,
Mikko
 
G

George Herold

Jan 1, 1970
0
Battery-connection straps are nickel.  1955-1981 Canadian nickels are
nickel.

Wow... excellent, I wonder if I can still find some in circulation if
I go to Canada.

George H.
 
G

George Herold

Jan 1, 1970
0
Ni-NiO-Ni tunnel junctions have barrier heights of about 0.2 eV.  This
behaviour in nickel is why nickel plated BNC connectors tend to be flaky
with low level signals.

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs
Principal Consultant
ElectroOptical Innovations LLC
Optics, Electro-optics, Photonics, Analog Electronics

160 North State Road #203
Briarcliff Manor NY 10510

hobbs at electrooptical dot nethttp://electrooptical.net

Oops, googling Ni-NiO tunneling
(item #3)
www.electrooptical.net/www/actj/NiNiONi.pdf

Not to be critcial, but the I-V looks ~90% resistive,
and worse at room temperature.

George H.
 
J

Jasen Betts

Jan 1, 1970
0
What experiment would demonstrate unequivocally that
light itself is conveyed by discrete photons?

Albert Einstein got the Nobel prize for it.
 
J

John Devereux

Jan 1, 1970
0
Jan Panteltje said:
Albert Einstein got the Nobel prize for it.


Look up which assholes got a peace [not so]nobel prize.

It is a political award, in this case awarded by the Jewish lobby,

That man was clueless and dies clueless, and admitted it before he freed humanity by passing away.
Unfortunately very large parts of humanity are still slaves of his dogma.

I like feynmanns "explanation" of explanations for things.

http://lesswrong.com/lw/99c/transcript_richard_feynman_on_why_questions/

I think this is the reason why we still get "no such thing as a photon"
or "Einstein was wrong". Otherwise known as "my common sense trumps your
100 years of experimental verifications".
 
J

John Devereux

Jan 1, 1970
0
Jan Panteltje said:
Jan Panteltje said:
On a sunny day (28 Mar 2013 11:02:31 GMT) it happened Jasen Betts

What experiment would demonstrate unequivocally that
light itself is conveyed by discrete photons?

Albert Einstein got the Nobel prize for it.


Look up which assholes got a peace [not so]nobel prize.

It is a political award, in this case awarded by the Jewish lobby,

That man was clueless and dies clueless, and admitted it before he freed humanity by passing away.
Unfortunately very large parts of humanity are still slaves of his dogma.

I like feynmanns "explanation" of explanations for things.

http://lesswrong.com/lw/99c/transcript_richard_feynman_on_why_questions/

I think this is the reason why we still get "no such thing as a photon"
or "Einstein was wrong". Otherwise known as "my common sense trumps your
100 years of experimental verifications".

Long time ago 10 years?
I downloaded the Feynman lectures videos that are free on the web.

[...]


So, anyways, after his corpuscles_of_light lecture, it became VERY
clear to me he was a good showman, a nice mathemagician, and probably
an excellent conman,

In other words, does not agree with your common sense.
He also got the wrong result, but only because he could not hack it,
(neither did Einstein) on Le Sage gravity.

Can you get "Le Sage" gravity to reproduce all the experimental
verifications of general relativity?

http://en.wikipedia.org/wiki/Tests_of_general_relativity
There is a distinct possibility that, as he once was in the bomb
program, he was deliberately spreading nonsense, to prevent other
world powers from obtaining the technology being developed in area 51,
or was it 52, probably 53 by now.

Anyways, that together with that other spin-head who's cat was half
dead (Schroedinger) set the stage for the worst physics or most
impressive obfuscation of reality I have ever heard about,

In short, be very careful to take mathematical probabilities for
reality, else somebody may 'prove' you actually are a mouse, at least
for infinitesimal short moments. Multiverses, no end to crap, I have
wormholes in my garden, with real worms.

And yet, *whenever* any of the not-common-sense predictions of quantum
mechanics are tested, it is that not-common-sense outcome that prevails.

If you are going to replace it all with something else, you have to be
able to reproduce all the verifications of otherwise unexplained
effects. And make your theory produce the observed parts per billion
agreement with experiment.

Saying "that's crap" does not cut it.
 
J

Jeroen Belleman

Jan 1, 1970
0
Jan Panteltje said:
What experiment would demonstrate unequivocally that
light itself is conveyed by discrete photons?

Albert Einstein got the Nobel prize for it.


Look up which assholes got a peace [not so]nobel prize.

It is a political award, in this case awarded by the Jewish lobby,

That man was clueless and dies clueless, and admitted it before he freed humanity by passing away.
Unfortunately very large parts of humanity are still slaves of his dogma.

I like feynmanns "explanation" of explanations for things.

http://lesswrong.com/lw/99c/transcript_richard_feynman_on_why_questions/

I think this is the reason why we still get "no such thing as a photon"
or "Einstein was wrong". Otherwise known as "my common sense trumps your
100 years of experimental verifications".

The debate has been going on for centuries. The photo-electric effect
is often mentioned as 'proof' that light is transmitted as photons.
This is not as conclusive as you might think. There is at least one
theory that does not need the concept of photons, written by another
physics Nobel prize winner, Willis Lamb. (In the sense that it
treats light as Maxwell's EM waves, but still ends up with energy
exchanges with matter in chunks of omega * hbar.)

The trouble with the photon view is that it challenges a number
of other commonly accepted concepts, such as the existence of a
finite maximum velocity of information transfer, the idea that
an object cannot be in several places at once, the belief that
an object has a definite state (the cat is either dead or alive),
and so on. I think it's well worth the effort to look for a
theory that does away with such problems.

Sure, QT gets all the right answers, but I find 'shut up and
calculate' singularly unsatisfying. To me, it has the distinct
flavour of epicycles, which also worked quite well, but lacked
the explanatory power of Newton's gravity. Despite the fact
that it does not tell what gravity *is*, but only how it works.
But there I'm with Feynman, in that all we can do to explain
what something is, is describing its appearance and behaviour.

Going against the concepts in vogue easily gets one passed off as
a crank and it requires a solid grasp of things to get one's ideas
accepted. I freely admit I don't have that, but I'm working on it.

Jeroen Belleman
 
M

Mr Stonebeach

Jan 1, 1970
0
This is not as conclusive as you might think. There is at least one
theory that does not need the concept of photons, written by another
physics Nobel prize winner, Willis Lamb. (In the sense that it
treats light as Maxwell's EM waves, but still ends up with energy
exchanges with matter in chunks of omega * hbar.)

Really? That sounds interesting. Do you have a pointer? I'm
aware of his anti-photon paper - is it in the references, maybe?
Going against the concepts in vogue easily gets one passed off as
a crank and it requires a solid grasp of things to get one's ideas
accepted. I freely admit I don't have that, but I'm working on it.

It's good you are doing it, at least you are justifying your views.
There's always a possibility that a simpler explanation exists,
and anyway, thought experiments strengthen ones 'gut level'
understanding of matters. It is often difficult to see through
a jungle of equations.

Still, I feel unlikely that any 'common sense' explanation
can shed light to such phenomena as the GHZ states -
but I'd be delighted proven wrong.

Regards,
Mikko
 
G

George Herold

Jan 1, 1970
0
On a sunny day (28 Mar 2013 11:02:31 GMT) it happened Jasen Betts
What experiment would demonstrate unequivocally that
light itself is conveyed by discrete photons?
Albert Einstein got the Nobel prize for it.
Look up which assholes got a peace [not so]nobel prize.
It is a political award, in this case awarded by the Jewish lobby,
That man was clueless and dies clueless, and admitted it before he freed humanity by passing away.
Unfortunately very large parts of humanity are still slaves of his dogma.
I like feynmanns "explanation" of explanations for things.

I think this is the reason why we still get "no such thing as a photon"
or "Einstein was wrong". Otherwise known as "my common sense trumps your
100 years of experimental verifications".

The debate has been going on for centuries. The photo-electric effect
is often mentioned as 'proof' that light is transmitted as photons.
This is not as conclusive as you might think. There is at least one
theory that does not need the concept of photons, written by another
physics Nobel prize winner, Willis Lamb. (In the sense that it
treats light as Maxwell's EM waves, but still ends up with energy
exchanges with matter in chunks of omega * hbar.)

The trouble with the photon view is that it challenges a number
of other commonly accepted concepts, such as the existence of a
finite maximum velocity of information transfer, the idea that
an object cannot be in several places at once, the belief that
an object has a definite state (the cat is either dead or alive),
and so on. I think it's well worth the effort to look for a
theory that does away with such problems.

Sure, QT gets all the right answers, but I find 'shut up and
calculate' singularly unsatisfying. To me, it has the distinct
flavour of epicycles, which also worked quite well, but lacked
the explanatory power of Newton's gravity. Despite the fact
that it does not tell what gravity *is*, but only how it works.
But there I'm with Feynman, in that all we can do to explain
what something is, is describing its appearance and behaviour.

Going against the concepts in vogue easily gets one passed off as
a crank and it requires a solid grasp of things to get one's ideas
accepted. I freely admit I don't have that, but I'm working on it.

Jeroen Belleman- Hide quoted text -

- Show quoted text -

Hi Jeroen, I wonder if you've read any of the stuff David Mermin has
been writing about the foundations of QM.
This is a bit long winded,
http://arxiv.org/abs/quant-ph/9801057
And lots of other things on the web.

(I'm a shut up and do the experiment type... Bell inequality
experiements are now moving into the udergrad physics labs.)

George H.
 
M

Mr Stonebeach

Jan 1, 1970
0
Some Japanese guys back in the 80s got a couple of dB of amplitude
squeezing by doing that with a diode laser, iirc.

Cheers

Phil Hobbs

Right, that was probably Yamamoto's work. Its details are beyond me,
I don't know lasers all that well, I just was interested in QND
measurements
at that time.

Anyway, the Tapster-Rarity-Satchell experiment is intriguiging. They
seem to utilize the feature of high-efficiency LEDs that whenever an
electron passes the junction, one photon is emitted. So, if you
can force the electrons to arrive to the junction in a correlated
manner, you would get out non-poissonian photon statistics. (This
makes me wonder - shouldn't the the junction capacitance act as
a charge reservoir which spoils the forced current? Well, I guess
one must just require the capacitive reactance to be larger than the
driver impedance at the average frequency of emission events).

My colleaques are doing something related, they are pumping single
electrons to get metrologically accurate current. Their pump is
driven
by an external oscillator, and it gives out pretty ideal antibunched
electron
flow. That pump wouldn't be practical for driving a LED, but it is a
demonstration
of a current source with a very low Fano factor - so they do
exist. (Well, there is always the metallic wire, of course...)

However T-R-S et al were simply driving the LED through a large
resistor,
and relied on Johnson current noise of the resistor being smaller
than
the junction shot noise. It is so simple that it approaches cheating!
Sound like, if the LED indicator lamps in your favourite electronic
gadget
have high-enough efficiency, they're likely emitting squeezed light!

The Fano factor deviation T-R-S saw was very small, however. I'm
wondering whether their effect is somehow related with the slight
bunching
which thermal light shows? The Johnson noise sort-of *is* blackbody
radiation, after all.

Regards,
Mikko
 
J

John Devereux

Jan 1, 1970
0
Jeroen Belleman said:
Jan Panteltje said:
On a sunny day (28 Mar 2013 11:02:31 GMT) it happened Jasen Betts

What experiment would demonstrate unequivocally that
light itself is conveyed by discrete photons?

Albert Einstein got the Nobel prize for it.


Look up which assholes got a peace [not so]nobel prize.

It is a political award, in this case awarded by the Jewish lobby,

That man was clueless and dies clueless, and admitted it before he freed humanity by passing away.
Unfortunately very large parts of humanity are still slaves of his dogma.

I like feynmanns "explanation" of explanations for things.

http://lesswrong.com/lw/99c/transcript_richard_feynman_on_why_questions/

I think this is the reason why we still get "no such thing as a photon"
or "Einstein was wrong". Otherwise known as "my common sense trumps your
100 years of experimental verifications".

The debate has been going on for centuries. The photo-electric effect
is often mentioned as 'proof' that light is transmitted as photons.
This is not as conclusive as you might think. There is at least one
theory that does not need the concept of photons, written by another
physics Nobel prize winner, Willis Lamb. (In the sense that it
treats light as Maxwell's EM waves, but still ends up with energy
exchanges with matter in chunks of omega * hbar.)

The trouble with the photon view is that it challenges a number
of other commonly accepted concepts, such as the existence of a
finite maximum velocity of information transfer

My understanding - such as it is - was that it did not actually allow
information to be transferred faster than light? None that is externally
accessible anyway.
, the idea that an object cannot be in several places at once, the
belief that an object has a definite state (the cat is either dead or
alive), and so on. I think it's well worth the effort to look for a
theory that does away with such problems.

Sure, but I think they have been looking for that for a long time
now. And the evidence for QM gets better and better, there are more and
more detailed and precise results that need to be reproduced. The
"explanation" or "mechanism" for QM is up for debate, but that was the
point Feynman was making I think. It does no good to have an
"explanation" using familiar objects and analogies, when it is those
very things you are trying to explain.
Sure, QT gets all the right answers, but I find 'shut up and
calculate' singularly unsatisfying. To me, it has the distinct
flavour of epicycles, which also worked quite well, but lacked
the explanatory power of Newton's gravity. Despite the fact
that it does not tell what gravity *is*, but only how it works.
But there I'm with Feynman, in that all we can do to explain
what something is, is describing its appearance and behaviour.

Going against the concepts in vogue easily gets one passed off as
a crank and it requires a solid grasp of things to get one's ideas
accepted. I freely admit I don't have that, but I'm working on it.

From what I have read Feynman was the ultimate "crank". He refused to
accept anything without deriving it himself or trying to explain it
himself. But you have to be really, really good to be able to do
that. And you have to know all of what is already known, all the
experiments that have already been done.
 
J

Jeroen Belleman

Jan 1, 1970
0
Really? That sounds interesting. Do you have a pointer? I'm
aware of his anti-photon paper - is it in the references, maybe?

It was a paper by Lamb and Scully (1968). Apparently it never made
it into a refereed journal, but the fact that it has Lamb's name
on it makes it worth reading. Copies float about on the web.

Regards,
Jeroen Belleman
 
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