Sources of quantum mechanics djvu

This interdisciplinary book should be of interest to scholars, teachers, and students in the fields of physics and philosophy of science. It examines the efforts by Sommerfeld and others to develop a new theory, now known as the old quantum theory. After some striking successes, this theory ran into serious difficulties and ended up serving as the scaffold on which the arch of modern quantum mechanics was built. This volume breaks new ground, both in its treatment of the work of Sommerfeld and his associates, and by offering new perspectives on classic papers by Planck, Einstein, Bohr, and others.

Paying close attention to both primary and secondary sources, Constructing Quantum Mechanics provides an in-depth analysis of the heroic struggle to come to terms with the wealth of mostly spectroscopic data that eventually gave us modern quantum mechanics. Recently, many universities have experimented by bringing quantum theory forward in the curriculum and we follow their example.

This book is intended to serve as an introduction to theoretical mechanics and quantum mechanics for chemists. I have included those parts of quantum mechanics which are of greatest fundamental interest and utility, and have developed those parts of classical mechanics which relate to and illuminate them.

I try to give a comprehensive treatment wherever possible. The book would acquaint chemists with the quantum structure of the basic object of chemistry, the atom. So we've done the experiment, you send a white electron into the hardness box, and we know that it's non-predictive, Now if you take the one that comes out the hard aperture, then you send it up here or send it up here, we know that these mirrors do nothing to the hardness of the electron except change the direction of motion.

We've already done that experiment. So you measure the hardness at the output, what do you get? Hard, because it came out hard, mirror, mirror, hardness, hard. And with soft, mirror, mirror, hardness, you know it comes out soft.

Was this the logic? How many people agree with this? How many people disagree? No abstention. So here's a prediction. Oh, yep. Could you justify that prediction without talking about oh, well, half the electrons were initially measured to be hard, and half were initially measured to be soft, by just saying, well, we have a hardness box, and then we joined these electrons together again, so we don't know anything about it.

So it's just like sending white electrons into one hardness box instead of two. So let's see. We're going to see in a few minutes whether that kind of an argument is reliable or not.

But so far we've been given two different arguments that lead to the same prediction, Like when you get them to where This is a very good question. So here's a question look you're sending a bunch of electrons into this apparatus. But if I take-- look, I took You take two electrons and you put them close to each other, what do they do?

They interact with each other through a potential, right? So yeah, we're being a little bold here, throwing a bunch of electrons in and saying, oh, they're independent.

So I'm going to do one better. I will send them in one at a time. One electron through the apparatus. And then I will wait for six weeks. See, you guys laugh, you think that's funny. But there's a famous story about a guy who did a similar experiment with photons, French guy. And, I mean, the French, they know what they're doing. So he wanted to do the same experiment with photons.

But the problem is if you take a laser and you shined it into your apparatus, there there are like, 10 to the 18 photons in there at any given moment. And the photons, who knows what they're doing with each other, right? So I want to send in one photon, but the problem is, it's very hard to get a single photon, very hard. So what he did, I kid you not, he took an opaque barrier, I don't remember what it was, it was some sort of film on top of glass, I think it was some sort of oil-tar film.

Barton, do you remember what he used? So he takes a film, and it has this opaque property, such that the photons that are incident upon it get absorbed. Once in a blue moon a photon manages to make its way through.

Literally, like once every couple of days, or a couple of hours, I think. So it's going to take a long time to get any sort of statistics. But he this advantage, that once every couple of hours or whatever a photon makes its way through. That means inside the apparatus, if it takes a pico-second to cross, triumph, right?

That's the week I was talking about. So he does this experiment. But as you can tell, you start the experiment, you press go, and then you wait for six months. Side note on this guy, liked boats, really liked yachts. So he had six months to wait before doing a beautiful experiment and having the results. So what did he do? Went on a world tour in his yacht. Comes back, collects the data, and declares victory, because indeed, he saw the effect he wanted.

So I was not kidding. We really do wait. So I will take your challenge. And single electron, throw it in, let it go through the apparatus, takes mere moments. Wait for a week, send in another electron. No electrons are interacting with each other. Just a single electron at a time going through this apparatus. Other complaints? I have a hard time resisting. So here's a prediction, We now have two arguments for this. So again, let's vote after the second argument.

You sure? How many people don't think so? Very small dust. It's correct. So, good. I like messing with you guys. So remember, we're going to go through a few experiments first where it's going to be very easy to predict the results. We've got four experiments like this to do. And then we'll go on to the interesting examples.

But we need to go through them so we know what happens, so we can make an empirical argument rather than an in principle argument. So there's the first experiment. Now, I want to run the second experiment.

And the second experiment, same as the first, a little bit louder, a little bit worse. The second experiment, we're going to send in hard electrons, and we're going to measure color at out. So again, let's look at the apparatus. We send in hard electrons. And our apparatus is hardness box with a hard and a soft aperture. And now we're going to measure the color at the output.

Color, what have I been doing? And now I want to know what fraction come out black, and what fraction come out white. We're using lots of monkeys in this process. OK, so this is not rocket science. Rocket science isn't that complicated.

Neuroscience is much harder. This is not neuroscience. So let's figure out what this is. So again, think about your prediction your head, come to a conclusion, raise your hand when you have an idea.

And just because you don't raise your hand doesn't mean I won't call on you. I like it. Tell me why. So the statement, I'm going to say that slightly more slowly.

That was an excellent argument. We have a hard electron. We know that hardness boxes are persistent. If you send a hard electron in, it comes out hard. So every electron incident upon our apparatus will transit across the hard trajectory. It will bounce, it will bounce, but it is still hard, because we've already done that experiment.

The mirrors do nothing to the hardness. So we send a hard electron into the color box, and what comes out? Well, we've done that experiment, too. Hard into color, So the prediction is This is your prediction. Is that correct? OK, let us vote. How many people think this is correct?

Gusto, I like it. How many people think it's not? All right. Yay, this is correct. Third experiment, slightly more complicated. But we have to go through these to get to the good stuff, so humor me for a moment. Third, let's send in white electrons, and then measure the color at the output port.

So now we send in white electrons, same beast. And our apparatus is a hardness box with a hard path and a soft path. Do-do-do, mirror, do-do-do, mirror, box, join together into our out.

And now we send those out electrons into a color box. And our color box, black and white. And now the question is how many come out black, and how many come out white. Again, think through the logic, follow the electrons, come up with a prediction.

Raise your hand when you have a prediction. And then it'll go back into the color box. But earlier when we did the same thing without the weird path-changing, it came out still. So I would say still So let me say that again, out loud. And tell me if this is an accurate extension of what you said. I'm just going to use more words. But it's, I think, the same logic.

We have a white electron, initially white electron. We send it into a hardness box. When we send a white electron into a hardness box, we know what happens.

Consider those electrons that came out the hard aperture. Those electrons that came out the hard aperture will then transit across the system, preserving their hardness by virtue of the fact that these mirrors preserve hardness, and end up at a color box.

We've done that experiment, too. The other half of the time, the single electron in the system will come out the soft aperture. It will then proceed along the soft trajectory, bounce, bounce, not changing its hardness, and is then a soft electron incident on the color box. But we've also done that experiment, and we get out, black and white. And the logic then leads to , twice, Was that an accurate statement?

It's a pretty reasonable extension. OK, let's vote. How many people agree with this one? OK, and how many people disagree? Yeah, OK.

So vast majority agree. And the answer is no, this is wrong. Never ever does an electron come out the black aperture. I would like to quote what a student just said, because it's actually the next line in my notes, which is what the hell is going on? So let's the series of follow up experiments to tease out what's going on here.

So something very strange, let's just all agree, something very strange just happened. We sent a single electron in. And that single electron comes out the hardness box, well, it either came out the hard aperture or the soft aperture.

And if it came out the hard, we know what happens, if it came out the soft, we know what happens. And it's not So we need to improve the situation. Hold on a sec. Hold on one sec. Well, OK, go ahead. So with the second hardness box, are we collecting both the soft and hard outputs? This guy? Oh, that's a mirror, not a hardness box. Oh, thanks for asking. Yeah, sorry. I wish I had a better notation for this, but I don't. There's a classic-- well, I'm not going to go into it.

Remember that thing where I can't stop myself from telling stories? So all this does, it's just a set of mirrors. It's a set of fancy mirrors. And all it does is it takes an electron coming this way or an electron coming this way, and both of them get sent out in the same direction. It's like a beam joiner, right? It's like a y junction. That's all it is. So if you will, imagine the box is a box, and you take, I don't know, Professor Zwiebach, and you put him inside.

And every time an electron comes up this way, he throws it out that way, and every time it comes in this way, he throws it out that way. And he'd be really ticked at you for putting him in a box, but he'd do the job well. It works reliably. So the question was, what's the difference between this experiment and the last one. Yeah, good question. So we're going to have to answer that.

So it's like as you weren't measuring it at all, right? Because we send in the white electron, and at the end we get out that it's still white. So somehow this is like not doing anything. But how does that work? So that's an excellent observation. And I'm going to build you now a couple of experiments that tease out what's going on. And you're not going to like the answer. I take a random source of electrons, I rub a cat against a balloon and I charge up the balloon. And so I take those random electrons, and I send them into a color box.

And we have previously observed that if you take random electrons and throw them into a color box and pull out the electrons that come out the white aperture, if you then send them into a color box again, they're still white. So that's how I've generated them. I could have done it by rubbing the cat against glass, or rubbing it against me, right, just stroke the cat. Any randomly selected set of electrons sent into a color box, and then from which you take the white electrons. So here's something I'm going to be very careful not to say in this class to the degree possible.

I'm not going to use the word to know. Measure is a very slippery word, too. I've used it here because I couldn't really get away with not using it. But we'll talk about that in some detail later on in the course. For the moment, I want to emphasize that it's tempting but dangerous at this point to talk about whether you know or don't know, or whether someone knows or doesn't know, for example, the monkey inside knows or doesn't know.

So let's try to avoid that, and focus on just operational questions of what are the things that go in, what are the things that come out, and with what probabilities.

And the reason that's so useful is that it's something that you can just do. There's no ambiguity about whether you've caught a white electron in a particular spot.

Now in particular, the reason these boxes are such a powerful tool is that you don't measure the electron, you measure the position of the electron. You get hit by the electron or you don't. And by using these boxes we can infer from their position the color or the hardness.

And that's the reason these boxes are so useful. So we're inferring from the position, which is easy to measure, you get beaned or you don't, we're inferring the property that we're interested in.

It's a really good question, though. Keep it in the back of your mind. And we'll talk about it on and off for the rest of the semester. This leads me into the next experiment. So here's the modification. But thank you, that's a great question. Here's the modification of this experiment. So let's rig up a small-- hold on, I want to go through the next series of experiments, and then I'll come back to questions. And these are great questions.

So I want to rig up a small movable wall, a small movable barrier. And here's what this movable barrier will do. If I put the barrier in, so this would be in the soft path, when I put the barrier in the soft path, it absorbs all electrons incident upon it and impedes them from proceeding. So you put a barrier in here, put a barrier in the soft path, no electrons continue through.

An electron incident cannot continue through. When I say that the barrier is out, what I mean is it's not in the way. I've moved it out of the way. So I want to run the same experiment. And I want to run this experiment using the barriers to tease out how the electrons transit through our apparatus. So experiment four. Let's send in a white electron again. I want to do the same experiment we just did. And color at out, but now with the wall in the soft path.

Wall in soft. So that's this experiment. So we send in white electrons, and at the output we measure the color as before.

And the question is what fraction come out black, and what fraction come out white. So again, everyone think through it for a second.

Just take a second. And this one's a little sneaky. So feel free to discuss it with the person sitting next to you. All right, now that everyone has had a quick second to think through this one, let me just talk through what I'd expect from the point of these experiments. And then we'll talk about whether this is reasonable. If it goes out the soft aperture, it's going to get eaten by the barrier, right?

It's going to get eaten by the barrier. However, here's an important bit of physics. And this comes to the idea of locality. I didn't tell you this, but these armlinks in the experiment I did, 3, kilometers long. That's too minor. Really long. Very long. Now, imagine an electron that enters this, an initially white electron. If we had the barriers out, if the barrier was out, what do we get?

We just did this experiment, to our surprise. And that means an electron, any electron, going along the soft path comes out white. Any electron going along the hard path goes out white. They all come out white.

So now, imagine I do this. Imagine we put a barrier in here 2 million miles away from this path. How does a hard electron along this path know that I put the barrier there? And I'm going to make it even more sneaky for you. I'm going to insert the barrier along the path after I launched the electron into the apparatus.

And when I send in the electron, I will not know at that moment, nor will the electron know, because, you know, they're not very smart, whether the barrier is in place. And this is going to be millions of miles away from this guy. So an electron out here can't know. It hasn't been there. It just hasn't been there. It can't know. But it can't possibly know whether the barrier's in there or not, right? It's over here. But all the electrons that do make it through must come out white, because they didn't know that there was a barrier there.

They didn't go along that path. Thank you, thank you, thank you, that was a slip of the tongue. I was making fun of the electron. So in that particular case, I was not referring to my or your knowledge. I was referring to the electron's tragically impoverished knowledge. AUDIENCE: But if they come out one at a time white, then wouldn't we know then with certainty that that electron is both hard and white, which is like a violation?

Then the electron would have demonstrably not go along the soft path. It would have demonstrably gone through the hard path, because that's the only path available to it. And yet, it would still have known that millions of miles away, there's a barrier on a path it didn't take. So which one's more upsetting to you? And personally, I find this one the less upsetting of the two. But they should all come out white, because those that didn't get eaten can't possibly know that there was a barrier here, millions of miles away.

So we run this experiment. And here's the experimental result. The barrier, if we put the barrier in the hardness path. How could the electron know? I'm making fun of it. AUDIENCE: So I guess my question is before we ask how it knows that there's a block in one of the paths, how does it know, before, over there, that there were two paths, and combine again?

So actually, this problem was there already in the experiment we did. All we've done here is tease out something that was existing in the experiment, something that was disturbing.

The presence of those mirrors, and the option of taking two paths, somehow changed the way the electron behaved.

How is that possible? And here, we're seeing that very sharply. Thank you for that excellent observation. So the question is basically, let's take this experiment, and let's make it even more intricate by, for example, replacing these mirrors by color boxes. So here's the thing I want to emphasize. I strongly encourage you to think through that example. And in particular, think through that example, come to my office hours, and ask me about it.

So that's going to be setting a different experiment. And different experiments are going to have different results. So we're going to have to deal with that on a case by case basis.

It's an interesting example, but it's going to take us a bit afar from where we are right now. But after we get to the punchline from this, come to my office hours and ask me exactly that question. How do you know the boxes work? These are the same boxes we used from the beginning. We tested them over and over. ALLAN ADAMS: How to say-- there's no other way to build a box that does the properties that we want, which is that you send in color and it comes out color again, and the mirrors behave this way.

Any box that does those first set of things, which is what I will call a color box, does this, too. There's no other way to do it. I don't mean just because like, no one's tested You take the electron that came out of the color box. That's what we mean by saying it's white. It's like, how do you know that my name is Allan? You say, Allan, and I go, what? But you're like, look that's not a test of whether I'm Allan. Pre-owned: Lowest price.. In this work, we illustrate the recently introduced concept of the cavity Born—Oppenheimer approximation [Flick et al.

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Quantum Mechanics and Quantum Field Theory and related topics. Two mechanisms are considered for first-order one-magnon light scattering: one involving a direct magnetic-dipole coupling and the other involving an The light scattering by these excitons are treated by extending the previous theory, which makers use of the spin-dependent electric polarizability, to include the degrees of freedom of the orbital angular momentum.

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Beginning in Loudon, The quantum theory of light, 3rd edition, Oxford Science Publica- tions, An electron is a quantum mechanical object and its spin should be treated quantum -mechanically The conventional representation of spin as a 3D spatial vector may tempt to apply the operational rules of a geometrical vector to spin, which is wrong for the most cases.

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Theory of the emission of long-wave light quanta by W. Pauli, M. The universal length appearing in the theory of elementary particles by W. The interaction between charged particles and the radiation field by H. In this paper, we propose a novel quantum multiple access technique based on optical coherent states. The information of several coherent state optical qubits is combined into a single qudit, which The quantum theory of light is an essential tool in the interpretation of measurements and in the understanding of the basic principles of quantum mechanics.

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Badolato, K. Hennessy, M. Atature et. Quantum Optics. Mesoscopic quantum optics. Fox Quantum Optics, An Introduction. Oxfors Press. A guide to Experiments in quantum optics. Loudon The quantum theory of light. Oxford Press. Syllabus Assessment Assessment Summative.

And what an introduction it was! His style is that of a smiling figure on horseback, cutting a clean way through, on a beautiful path, with a swift bright sword. Some years ago I was asked, like others, I am sure, to present to the Library of the American Philosophical.

Here is an unordered list of online physics books available for free download. There are books covering the areas of classical mechanics, thermodynamics, electromagnetism, optics, quantum physics, atomic and nuclear physics, astrophysics, and more. The books are stored in various formats for downloading …. I study string theory and its applications to gravity, quantum gravity, and condensed matter physics.

Quantum mechanics, this is a course in quantam mechanics. Quantam mechanics Is my daily language. Quantum mechanics is my old friend. I met quantum mechanics 20 years ago. I just realized that last night. It was kind of depressing.