Does anyone have any advice to how to go about learning more about quantum mechanics?
I have an engineering background, and have been trying to get a broad sense of the calculus of variations, the wave equation, and hamiltonian mechanics and their context while trying to delve more specifically into lagrangian mechanics.
My mathematics background is a little soft at this point. It's been almost a decade since I've taken any math class, but I have a reasonable working knowledge of multivariable calculus (greens theorem, stokes theorem, divergence) and differential equations (ODE), though my knowledge of linear algebra is next to nothing at this point.
This is all for personal interest. Does anyone have any specific suggestions on where to begin?
I would go to the library and check out books.
Look online for recommended physics books. One off the top of my head is The Elegant Universe.
Check out youtube/MIT for videos of classes about quantum physics.
Check out some Discovery Science for some videos about it.
Check out your local college. We had older people in my classes. I'm sure you could atleast watch one.
If you're near a university you could audit classes.
Or you could see if there are any lectures involved in MIT's online lecture series. Is that still free to use?
There are a couple of free options that MIT offers. There's OpenCourseWare, which is basically just a repository for past course materials that you can use to teach yourself. A quick search revealed three undergraduate classes from the physics department (Quantum Physics I, Quantum Physics II, and Quantum Physics III) and two graduate classes from the chemistry department (Quantum Mechanics I and Quantum Mechanics II). MIT is also part of the edX program, which brings complete classes (materials, lecture videos, etc.) from top schools online for free. The program is still new and the selection of classes is small (nothing dedicated to quantum mechanics at this point), but it may be something to watch for in the future.
You definitely have a background in Math when describing Lagrange and Hamiltonian The most difficult part of Linear Algebra you might remember is copying everything into tables and not making mistakes.
I would have recommended any of the feel good quantum mechanics PBS programs with Brian Green, but if you're looking for more than "look at how weird and unpredictable our world is!" we'll have to google a little deeper. I myself still have my textbook on composition of matter, but I'm afraid I didn't get too much out of my quantum studies.
Here is my favorite hit off a quick google search for an equation intensive look at QM. Starting with De Broglie wavelength since it's the most fun part of the topic. Imagine going out to dinner and convincing your friends that they are in fact a wave, and when you're not looking at them they fluctuate like this " "
Chapter 4 is a good read for that Linear Algebra you're afraid of. Leads into some intimidating math and then leads into all that uncertainty business you hear about.
Chapter 5 section 2 titled the Schrodinger Wave Equation is the next really important/famous aspect of QM. The Big Bang Theory (show) has affectionately used Schrodinger's Cat as a symbol to get past uncertainty and just "open the box" as they say.
Don't give up if it's a little too dry to get through it all. They're lecture notes. I expect the internet will be brimming with Quantum Physics explanations with the excitement surrounding the Higgs particle.
Introduction to Quantum Mechanics by Griffiths is the book you want, it's $13 if you order the international edition and as long as you have some background in partial differential equations and linear algebra, you should be able to get a grasp on a lot of it.
I say this book because it is pretty much what every physics undergrad uses in their study of quantum mechanics.
The biggest thing is, you have to stop thinking of physics as something physical, when dealing with quantum mechanics, you follow the math and out pops real truths which often don't make sense.
I would say just taking a course in Quantum Mechanics is the way to go. I could probably have self taught myself just about everything in college... except for quantum. Or at least, I got so much more out of it by taking a course on it.
I think self teaching it could lead you to believe some major misconceptions. It is not an intuitive topic, it is all based on math.
Here is my favorite hit off a quick google search for an equation intensive look at QM. Starting with De Broglie wavelength since it's the most fun part of the topic. Imagine going out to dinner and convincing your friends that they are in fact a wave, and when you're not looking at them they fluctuate like this " "
Just be careful in your understanding of this, the particle isn't traveling like a wave, the probability of finding the particle in a certain location is what is waving...it's weird.
I'm just a lowly liberal arts guy, but you might want to check out The Elegant Universe from Nova. They did a bit about the "Quantum Cafe" that was pretty interesting.
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Just be careful in your understanding of this, the particle isn't traveling like a wave, the probability of finding the particle in a certain location is what is waving...it's weird.
Something about this doesn't seem right. Particles also behave as waves. Particle-wave duality doesn't stem from the shape of the probability function which seems to be what you are saying.
I think this is the easiest way to explain it. From wikipedia on wave-particle duality...
Wave–particle duality is deeply embedded into the foundations of quantum mechanics, so well that modern practitioners rarely discuss it as such. In the formalism of the theory, all the information about a particle is encoded in its wave function, a complex-valued function roughly analogous to the amplitude of a wave at each point in space. This function evolves according to a differential equation (generically called the Schrödinger equation), and this equation has solutions that follow the form of the wave equation. Propagation of such waves leads to wave-like phenomena such as interference and diffraction.
The particle-like behavior is most evident due to phenomena associated with measurement in quantum mechanics. Upon measuring the location of the particle, the particle will be forced into a more localized state as given by the uncertainty principle. When viewed through this formalism, the measurement of the wave function will randomly "collapse", or rather "decohere", to a sharply peaked function at some location. The likelihood of detecting the particle at any particular location is equal to the squared amplitude of the wave function there. The measurement will return a well-defined position, (subject to uncertainty), a property traditionally associated with particles.
The particle isn't really traveling as a wave, think of it more as a cloud that travels that when you look at it, it collapses to a certain point with regards to the uncertainty principle. The location that it collapses to is dependent upon the wave function for that particle which describes the probability of it being in any location as it moves through space and oftentimes time.
The de Broglie wavelength is really the wavelength of the probability function. It behaves like the particle travels as a wave but current physics doesn't see it that way.
You can probably learn a lot from books and tutorials. Local community college course even.
But I'm confused. Back in the probability thread on dice, you implied that your quantum mechanics knowledge contributed to bad intuition on the dice problem. Or maybe I'm confusing you with somebody else. Probably my bad.
You can probably learn a lot from books and tutorials. Local community college course even.
But I'm confused. Back in the probability thread on dice, you implied that your quantum mechanics knowledge contributed to bad intuition on the dice problem. Or maybe I'm confusing you with somebody else. Probably my bad.
It was me, the problem was I confused the dice as being identical with being indistinguishable which is not the same.
I think this is the easiest way to explain it. From wikipedia on wave-particle duality...
The particle isn't really traveling as a wave, think of it more as a cloud that travels that when you look at it, it collapses to a certain point with regards to the uncertainty principle. The location that it collapses to is dependent upon the wave function for that particle which describes the probability of it being in any location as it moves through space and oftentimes time.
The de Broglie wavelength is really the wavelength of the probability function. It behaves like the particle travels as a wave but current physics doesn't see it that way.
Part of the disconnect is probably that LogicX and I are chemists, not physicists. Having established that...
How is this reconciled with the observation of interference from something like the double-slit experiment? The "particle" itself has to have wave-like character to explain the interference pattern....or (I'm typing this as I'm thinking; forgive the shift) is it that the interference pattern is a "physical" manifestation if the probability? Interference is seen because the probabilities are different at different locations and are affected by the other particles traveling through the slits?
The double slits affect the wave functions because the area around the slits are potential barriers, this causes the probability function to take on the form of the interference pattern. It isn't that one electron (in this example) is forming the pattern on its own, it is that all the electrons have certain probabilities to end up at certain points and they are more likely to end up at the center of each fringe.
Ah. A question I am uniquely qualified to answer here. I, too, am a heat transfer mechanical engineer with similar interests. Eventually, it is my intent to acquire a PhD in quantum. I started by taking an introduction to modern physics course to see if I even liked it and the answer is...I love it. If you have the heat transfer background, then I highly recommend having a gander at solid state physics and going from there. It is essentially applied quantum mechanics and an engineer should be able to understand it a bit better than someone with a physics background.
I think this is the easiest way to explain it. From wikipedia on wave-particle duality...
The particle isn't really traveling as a wave, think of it more as a cloud that travels that when you look at it, it collapses to a certain point with regards to the uncertainty principle. The location that it collapses to is dependent upon the wave function for that particle which describes the probability of it being in any location as it moves through space and oftentimes time.
The de Broglie wavelength is really the wavelength of the probability function. It behaves like the particle travels as a wave but current physics doesn't see it that way.
I understand how the wave function collapses and the probability function. But I take issue with the idea that it isn't really traveling as a wave. Take the double slit experiment for example. Particles in this case behave as a wave, so to say that they are not waves seems puzzling.
EDIT: The minds of chemists really are alike, I see Viricide already thought of the double slit experiment.
With light, the actual electomagnetic waves are interfering. With particles, its the probability waves that interfere and change the wave function due to the potential barriers that make up the slits.
With light, the actual electomagnetic waves are interfering. With particles, its the probability waves that interfere and change the wave function due to the potential barriers that make up the slits.
You'll have to forgive me since my background is not strongly in quantum mechanics. But I'm having trouble deciphering this in regards to the claim that particles act as waves.
The double slits affect the wave functions because the area around the slits are potential barriers, this causes the probability function to take on the form of the interference pattern. It isn't that one electron (in this example) is forming the pattern on its own, it is that all the electrons have certain probabilities to end up at certain points and they are more likely to end up at the center of each fringe.
Interference of individual particles
An important version of this experiment involves single particles (or waves — for consistency, they are called particles here). Sending particles through a double-slit apparatus one at a time results in single particles appearing on the screen, as expected. Remarkably, however, an interference pattern emerges when these particles are allowed to build up one by one (see the image to the right). For example, when a laboratory apparatus was developed that could reliably fire one electron at a time through the double slit,[14] the emergence of an interference pattern suggested that each electron was interfering with itself, and therefore in some sense the electron had to be going through both slits at once[15] — an idea that contradicts our everyday experience of discrete objects. This phenomenon has also been shown to occur with atoms and even some molecules, including buckyballs.[10][16][17] So experiments with electrons add confirmatory evidence to the view of Dirac that electrons, protons, neutrons, and even larger entities that are ordinarily called particles nevertheless have their own wave nature and even their own specific frequencies.
So...is this a case of ambiguous/poor wording? Does an interference pattern really emerge with a single particle?
With light, the actual electomagnetic waves are interfering. With particles, its the probability waves that interfere and change the wave function due to the potential barriers that make up the slits.
Why is light different? Is there a property of photons that makes the explanation different than it is for other particles? It makes intuitive sense to me that light would interfere electromagnetically while "matter" particles would do so probabilistically, but what's the physics behind that?
Light is different because light is a wave that has particle like properties and things like electrons are particles that have wave like properties. Just because they have similar properties to each other does not mean they are the same thing.
Also, it isn't that the electron is interfering with itself, its that the slits alter the wave function.
Light is different because light is a wave that has particle like properties and things like electrons are particles that have wave like properties. Just because they have similar properties to each other does not mean they are the same thing.
That makes sense intuituvely, but why? What defines what it "is" versus what it has properties of? Does that make any sense? I'm not dumb; I know having similar properties doesn't make things the same, so there's no need to condescend. This just isn't my area of expertise, and it's been years since I've touched any physics.
I don't get the distinction between "a wave that has particle like properties and particles that have wave like properties." Defining something that has both wave and particle properties as either a wave or particle seems meaningless and ambiguous in the context of quantum mechanics.
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I have an engineering background, and have been trying to get a broad sense of the calculus of variations, the wave equation, and hamiltonian mechanics and their context while trying to delve more specifically into lagrangian mechanics.
My mathematics background is a little soft at this point. It's been almost a decade since I've taken any math class, but I have a reasonable working knowledge of multivariable calculus (greens theorem, stokes theorem, divergence) and differential equations (ODE), though my knowledge of linear algebra is next to nothing at this point.
This is all for personal interest. Does anyone have any specific suggestions on where to begin?
Or you could see if there are any lectures involved in MIT's online lecture series. Is that still free to use?
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Look online for recommended physics books. One off the top of my head is The Elegant Universe.
Check out youtube/MIT for videos of classes about quantum physics.
Check out some Discovery Science for some videos about it.
Check out your local college. We had older people in my classes. I'm sure you could atleast watch one.
There are a couple of free options that MIT offers. There's OpenCourseWare, which is basically just a repository for past course materials that you can use to teach yourself. A quick search revealed three undergraduate classes from the physics department (Quantum Physics I, Quantum Physics II, and Quantum Physics III) and two graduate classes from the chemistry department (Quantum Mechanics I and Quantum Mechanics II). MIT is also part of the edX program, which brings complete classes (materials, lecture videos, etc.) from top schools online for free. The program is still new and the selection of classes is small (nothing dedicated to quantum mechanics at this point), but it may be something to watch for in the future.
If a physical book is more your style, I enjoyed Quantum Theory: A Very Short Introduction as a simple introduction that I could grasp as a freshman in college.
I would have recommended any of the feel good quantum mechanics PBS programs with Brian Green, but if you're looking for more than "look at how weird and unpredictable our world is!" we'll have to google a little deeper. I myself still have my textbook on composition of matter, but I'm afraid I didn't get too much out of my quantum studies.
Here is my favorite hit off a quick google search for an equation intensive look at QM. Starting with De Broglie wavelength since it's the most fun part of the topic. Imagine going out to dinner and convincing your friends that they are in fact a wave, and when you're not looking at them they fluctuate like this " "
Chapter 4 is a good read for that Linear Algebra you're afraid of. Leads into some intimidating math and then leads into all that uncertainty business you hear about.
Chapter 5 section 2 titled the Schrodinger Wave Equation is the next really important/famous aspect of QM. The Big Bang Theory (show) has affectionately used Schrodinger's Cat as a symbol to get past uncertainty and just "open the box" as they say.
Don't give up if it's a little too dry to get through it all. They're lecture notes. I expect the internet will be brimming with Quantum Physics explanations with the excitement surrounding the Higgs particle.
I say this book because it is pretty much what every physics undergrad uses in their study of quantum mechanics.
The biggest thing is, you have to stop thinking of physics as something physical, when dealing with quantum mechanics, you follow the math and out pops real truths which often don't make sense.
I think self teaching it could lead you to believe some major misconceptions. It is not an intuitive topic, it is all based on math.
Just be careful in your understanding of this, the particle isn't traveling like a wave, the probability of finding the particle in a certain location is what is waving...it's weird.
EDH:
UR Niv-Mizzet's Madness
BGW Ghave's Garden
WUBRG Karona's Chaos
Retired: Too damn many to count
Vintage:
URWelder
WUBRG Dredge
Kitchen Table:
B Zombies in Your Head
Something about this doesn't seem right. Particles also behave as waves. Particle-wave duality doesn't stem from the shape of the probability function which seems to be what you are saying.
The particle isn't really traveling as a wave, think of it more as a cloud that travels that when you look at it, it collapses to a certain point with regards to the uncertainty principle. The location that it collapses to is dependent upon the wave function for that particle which describes the probability of it being in any location as it moves through space and oftentimes time.
The de Broglie wavelength is really the wavelength of the probability function. It behaves like the particle travels as a wave but current physics doesn't see it that way.
But I'm confused. Back in the probability thread on dice, you implied that your quantum mechanics knowledge contributed to bad intuition on the dice problem. Or maybe I'm confusing you with somebody else. Probably my bad.
It was me, the problem was I confused the dice as being identical with being indistinguishable which is not the same.
How is this reconciled with the observation of interference from something like the double-slit experiment? The "particle" itself has to have wave-like character to explain the interference pattern....or (I'm typing this as I'm thinking; forgive the shift) is it that the interference pattern is a "physical" manifestation if the probability? Interference is seen because the probabilities are different at different locations and are affected by the other particles traveling through the slits?
Credit to DolZero for this awesome sig!
I understand how the wave function collapses and the probability function. But I take issue with the idea that it isn't really traveling as a wave. Take the double slit experiment for example. Particles in this case behave as a wave, so to say that they are not waves seems puzzling.
EDIT: The minds of chemists really are alike, I see Viricide already thought of the double slit experiment.
You'll have to forgive me since my background is not strongly in quantum mechanics. But I'm having trouble deciphering this in regards to the claim that particles act as waves.
That makes sense.
So, for a curve-ball...
So...is this a case of ambiguous/poor wording? Does an interference pattern really emerge with a single particle?
Edit Why is light different? Is there a property of photons that makes the explanation different than it is for other particles? It makes intuitive sense to me that light would interfere electromagnetically while "matter" particles would do so probabilistically, but what's the physics behind that?
Also, it isn't that the electron is interfering with itself, its that the slits alter the wave function.