Exact solution of the double slit experiment with a single photon

[mma]

Hi,

Could somebody, please, give a reference for the exact derivation of the single-photon double-slit experiment? I mean similar then the well-known solution for the particle-in-box, or for the Hydrogen-atom. That is, starting from the Schrödinger-equation, taking boundary conditions representing the double slit, and the solution is the values of the state function on the plane behind the slits. The best would be a web link.

The same for a single electron is also interested.

Thank you in advance!

mma

 

[ZapperZ]

Try T.V. Marcella, Eur. J. Phys., v.23, p.615 (2002).

Zz.

 

[mma]

Thank you very much! This article is very instructive, however it consists of rather heuristic considerations then beeing an exact solution.

The author tells that he unaware of any exact description of the slit interference except one, witch uses Feynman's path integral method:
http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=AJPIAS000060000010000896000001&idtype=cvips&gifs=yes" .

Unfortunately, both article are available for subscribers, or for money, and I am not a subscriber and also not in abundance of of the latter. At last I managed to get the first one from one of my acquaintance, but it would be awkward to ask this second one from him too. May I ask you to send me this article, please?

 

[koantum]

Could somebody, please, give a reference for the exact derivation of the single-photon double-slit experiment? I mean similar then the well-known solution for the particle-in-box, or for the Hydrogen-atom. That is, starting from the Schrödinger-equation

This is not always the best way to start. Check out http://thisquantumworld.com/PDF/2slits.zip" of The Quantum Challenge by Greenstein and Zajonc (a highly recommendable book). (Save target/link - a zip file containing tiff files.) From the preface of this book: "In every textbook we know, quantum mechanics has been largely sanitized of these beautiful enticements and their implications. This book is intended to complement these accounts with a broader range of considerations."

 

[koantum]

More relevant papers:

• Sudarshan, E.C.G and Rothman, Tony: The two-slit interferometer reexamined, Am. J. Phys. 59 (7), pp. 592-595 (1991).
• Jones, D G C: Two slit interference -- classical and quantum pictures, Eur. J. Phys. 15, pp. 170-178 (1994)

The central issue in both papers is that the classical limit of photon interference is tricky owing to the fact that what is interfering is coherent states rather than states with definite photon numbers. The interference experiment with electrons (one at a time, as done by Tonomura, A., Endo, J., Matsuda, T., and Kawasaki, T.: "Demonstration of single-electron buildup of an interference pattern,'' Am. J. Phys 57 (2), pp. 117-120.)

 

[mma]

More relevant papers:

• Sudarshan, E.C.G and Rothman, Tony: The two-slit interferometer reexamined, Am. J. Phys. 59 (7), pp. 592-595 (1991).
• Jones, D G C: Two slit interference -- classical and quantum pictures, Eur. J. Phys. 15, pp. 170-178 (1994)

The central issue in both papers is that the classical limit of photon interference is tricky owing to the fact that what is interfering is coherent states rather than states with definite photon numbers. The interference experiment with electrons (one at a time, as done by Tonomura, A., Endo, J., Matsuda, T., and Kawasaki, T.: "Demonstration of single-electron buildup of an interference pattern,'' Am. J. Phys 57 (2), pp. 117-120.)

You mean
"[URL The two-slit interferometer reexamined,'' by E. C. G. Sudarshan and T. Rothman [Am. J. Phys. 59, 592–595 (1991)]
[/URL],
http://www.iop.org/EJ/abstract/0143-0807/15/4/003"
and
"[URL Tonomura, J. Endo, T. Matsuda, and T. Kawasaki, Demonstration of single-electron buildup of an interference pattern - American Journal of Physics -- February 1989 -- Volume 57, Issue 2, pp. 117-120
[/URL]

All of them are available for subscribers, or for money :(


The quoted section from Greenstein and Zajonc's book is really a good introduction for the theme, thank you for it.

 

[CarlB]

"Exact derivations" are not available for a lot of differential equations. The usual calculations are unsatisfying in that they give the values for the wave function only on the surface of the target. That is, they rely on the superposition principle. If one could be satisfied with an approximate derivation that gave the value of the wave function at all positions, then the Bohmian mechanics have those, though their notation is odd. For example:
http://www.mathematik.uni-muenchen.de/~bohmmech/Poster/post/postE.html

As an aside, I am convinced that the superposition principle is not a fundamental part of the physical reality, but instead appears only because of the mathematics. This is because I "believe" in density matrices instead of wave functions. So to me, the superposition principle is just a handy way of finding new and interesting solutions to the mathematics problem of finding solutions to Schroedinger's equation (the same for Dirac's eqn, etc.) and is not an indication of the nature of reality per se.

The drunk, upon losing his keys at night, looks under the lamp post first, and explores the darkness later. And so the physics community begins with the linearized theory rather than the bilinear.

Carl

 

[koantum]

All of them are available for subscribers, or for money :(

My copies of them are lousy, otherwise I would have scanned and uploaded them too.

 

[Schrodinger's Dog]

Unfortunately, both article are available for subscribers, or for money, and I am not a subscriber and also not in abundance of of the latter. At last I managed to get the first one from one of my acquaintance, but it would be awkward to ask this second one from him too. May I ask you to send me this article, please?

Indeed I had the same problem with finding info when I was looking into this area, it really is very frustrating, science is for the rich and the scientist it seems

I think if I ever live long enough to retire I might create a website with all the seminal papers of the last 600 years for free . Of course I'd be shut down in a week, and probably jailed, but it'd be worth it just to get the information into the aether. For the poor interested laymen and poor undergraduates out there j/k

In this country you read for a degree, unfortuanately you don't have acces to information that might be of relevance sometimes and it bites

 

[ZapperZ]

Indeed I had the same problem with finding info when I was looking into this area, it really is very frustrating, science is for the rich and the scientist it seems

I think if I ever live long enough to retire I might create a website with all the seminal papers of the last 600 years for free . Of course I'd be shut down in a week, and probably jailed, but it'd be worth it just to get the information into the aether. For the poor interested laymen and poor undergraduates out there j/k

In this country you read for a degree, unfortuanately you don't have acces to information that might be of relevance sometimes and it bites

Please note that MOST UNIVERSITIES and LIBRARIES tend to have SITE WIDE ACCESS to most of these journals. This is true for Science, Nature, Physical Reviews, etc... etc. So think again! Go to a library in a university, get to a terminal, and check if you can get access to these journals! Often, just being on a campus computer network allows you to get access to these journals! If your school subscribes to the hard copy edition of the Physical Review journals, for example, and does not have site-wide access, then someone in charge of your library acquisition is not doing his/her job. PR makes it so easy to get one of these with the hardcopy subscription.

Zz.

 

[ZapperZ]

You mean
"[URL The two-slit interferometer reexamined,'' by E. C. G. Sudarshan and T. Rothman [Am. J. Phys. 59, 592–595 (1991)]
[/URL],
http://www.iop.org/EJ/abstract/0143-0807/15/4/003"
and
"[URL Tonomura, J. Endo, T. Matsuda, and T. Kawasaki, Demonstration of single-electron buildup of an interference pattern - American Journal of Physics -- February 1989 -- Volume 57, Issue 2, pp. 117-120
[/URL]

All of them are available for subscribers, or for money :(

PM me your e-mail address and I'll send them to you if you still couldn't get them.

Zz.

 

[Schrodinger's Dog]

Please note that MOST UNIVERSITIES and LIBRARIES tend to have SITE WIDE ACCESS to most of these journals. This is true for Science, Nature, Physical Reviews, etc... etc. So think again! Go to a library in a university, get to a terminal, and check if you can get access to these journals! Often, just being on a campus computer network allows you to get access to these journals! If your school subscribes to the hard copy edition of the Physical Review journals, for example, and does not have site-wide access, then someone in charge of your library acquisition is not doing his/her job. PR makes it so easy to get one of these with the hardcopy subscription.

Zz.

That's the only problem with the Open University the library is only on line, unless you fancy hopping on a train to Milton Keyens, about 60 miles away. Which means searching for any journal is very time consuming. And I still can't find many papers people post in here, in fact it's rare if I can find any at all, and I rarely have time to do an extensive search anyway. What people at university or in academia or in any scientific field fail to realize that is not every university has the breadth theirs does and not every student has easy access to a library. I find the difficulty in getting access to papers an inconvenience atm, but as I progress no doubt it will frustrate me more and more. thus the joke about having acces to all these papers on one web site, if only copyright and intellectual property laws allowed that

 

[ZapperZ]

That's the only problem with the Open University the library is only on line, unless you fancy hopping on a train to Milton Keyens, about 60 miles away. Which means searching for any journal is very time consuming. And I still can't find many papers people post in here, in fact it's rare if I can find any at all, and I rarely have time to do an extensive search anyway. What people at university or in academia or in any scientific field fail to realize that is not every university has the breadth theirs does and not every student has easy access to a library. I find the difficulty in getting access to papers an inconvenience atm, but as I progress no doubt it will frustrate me more and more. thus the joke about having acces to all these papers on one web site, if only copyright and intellectual property laws allowed that

Then those are the CHOICES that you have made to do what you are doing. Unless you can contact the library ask make a request for such papers, you are stuck with whatever it is that you have. And if such things are inaccessible to you, then it is obvious that your institution does not have the ability to fully support such means. The fault here then does not lie with the journals or even other institutions that provide such access.

Zz.

 

[inha]

My university offers a proxy server service which allows students and staff access all the subscribed journals via home computers. Maybe you should check if they have something similiar.

 

[Schrodinger's Dog]

No we can only blame the fault of ease of acquisition of information on sociological factors. You could probably throw wealth in there, it must be so nice to be able to chose to go to university of your choice and wrack up £20,000 worth of debt. Me I'm stuck with working to finance my studies. I suspect that is of course my fault too.

 

[ZapperZ]

No we can only blame the fault of ease of acquisition of information on sociological factors. You could probably throw wealth in there, it must be so nice to be able to chose to go to university of your choice and wrack up £20,000 worth of debt. Me I'm stuck with working to finance my studies. I suspect that is of course my fault too.

Then you have missed my point entirely. Note what you said EARLIER:

Indeed I had the same problem with finding info when I was looking into this area, it really is very frustrating, science is for the rich and the scientist it seems

I think if I ever live long enough to retire I might create a website with all the seminal papers of the last 600 years for free . Of course I'd be shut down in a week, and probably jailed, but it'd be worth it just to get the information into the aether. For the poor interested laymen and poor undergraduates out there j/k

In this country you read for a degree, unfortuanately you don't have acces to information that might be of relevance sometimes and it bites.

You make it seem as if you are justified in "punishing" scientific journals just because you are deprived of having free access to everything you want. My point is that it is NOT the fault of these journals that you do not have access to them. If you go to a music school, but you don't have access to a physics journal, well DUH! If you go to a school that for some reason does NOT have any means for you to get access to the things you need as PART of your academic work, then the fault lies with THAT institution, not the journal! Have you, for example, tried contacting the library and see if you can request a particular paper? No? Yes?

The academic support system is supposed to be there for THAT particular purpose. If such a support can't be provided, then something is wrong and the "blame", if any, lies there, and not at the source of info.

And take note, many journals grant authors the right to put the published paper on the authors webpages, or to distribute to people who request a copy of a paper for academic/research purposes. Have you tried contacting these authors and request a reprint? No? Yes?

And yes, you are right if I sound annoyed by this. I'm one of those people who simply can't stand people who simply whine and complain about things without exhausting all possible avenues. If it means THAT much to you, go and try to GET it and not simply expect things to just fall onto your lap!

Zz.

 

[Schrodinger's Dog]

Yes I have tried all means necessary, and sorry they are just not available without paying, and I find that - maybe wrongly - annoying, but as I'm in limbo between a maths course and the physics course I only have access to maths papers and even if I did have access to physics papers many of the more obscure ones I still would have to pay for, not only that but I suspect that external UK journals would not be available.

And I am not whining, what bothers me at all is that the information is locked away at all. I'd prefer it if everyone or anyone can get acces to papers, particularly old papers say more than 20 years old, but unfortunately the world doesn't work that way. Yes it's a quantum leap since the internet has opened up research to all, but unfortunately no sooner had this wealth of knowledge been opened to people than the charges for it came in and robbed some people of access. OK I'm a socialist about information, I think new papers rightly have the right to be locked up tight, but I fail to see why some journals aren't making things more accessable? If they are doing this then I apologise, but I've yet to see much evidence, perhaps I'm looking in the wrong place, some advice would be nice?

If it's whining to feel a little annoyed that information is available to few and not many then I can live with that.

Thus my jibe about information being only available to those who can afford to access it.

I have since found out from an independant source that you can pay for access to University libraries as a member of the public(alot less than having to individually pay for papers) and gain access to their resources. This sort of advice may prove priceless. Telling me it's not the journal's fault and to stop whining: not so valuable. But thanks for the thought anyway.

Only problem here is my local university closed it's physics dept through lack of student numbers and lack of funding. Which means I have to travel 20 miles to pick up a paper. Doable and better than 60.

 

[koantum]

I have since found out from an independant source that you can pay for access to University libraries as a member of the public(alot less than having to individually pay for papers) and gain access to their resources.

Hi doggy,
Tell us what you find out. We here (in India) have a Government service known as NISCAIR where I can mail order hard copies of research papers at a very nominal cost. If any Indian library has it, I can get it.

 

[Schrodinger's Dog]

Yeah, I have also been told that their are certain web intermediate business's that will supply papers for a yearly subscription, which would also help alot.