As a chemistry lecturer, for years I've been searching for a lecture series that goes beyond saying that qm is weird and never showing why. Thanks. I'll be watching and rewatching for some time.
DrPhysicsA, I believe you had said that you are going to make a series on string theory, although I may be mistaken. I would be grateful if you can say something about when they will be uploaded.
Sayan Datta I have no immediate plans to make any series on string theory. My aim is to try to keep things simple and frankly I can't think of a way of getting the simplicity required into string theory. I am currently working on a short series on nuclear physics.
Thanks for making these awesome playlists of physics lectures. I have watched all of your videos in Quantum Mechanics and those are very well organized and good.
When replacing the position operator with position (which makes sense), why don't you also replace the momentum operator with momentum? I was first confused with why you can't do this for momentum when you were finding the commutator of the p and x operators...THanks!
Love your approach to teaching quantum mechanics. I wished u could do one on solid state physics. Would have loved it. You made quantum easier for me. Thank you a lot.
I like your videos very much. Please keep on doing these lessons. It would be nice if you could add a series about the solution of the Schrödinger equation for a hydrogen atom. It's a masterpiece of mathematics to calculate the solution in sperical coordinates and to end up with measured energy levels. I would appreciate it very much.
Thanks, Doctor. Brilliant clarity, though you might have made explicit the origin of zero point energy here. Love your thorough style. This series has helped me make sense out of Susskind's video lectures from Stanford (OMG).
Absolutely love your videos! I was just wondering if someone could help me out- I'm not sure why we can use the equation 1/2 (omega)^2mx^2 for the potential of a particle? We derived this from looking at a mass- spring system, and so I don't see why this would be valid for a single particle, especially considering we do not know what potential the particle is in. If the particle in question is an electron around the nucleus of an atom, then the potential certainly will not be 1/2 (omega)^2mx^2 so why is this used in the Hamiltonian? Thank you for any answers, and thank you DrPhysicsA for your brilliant videos!!!
A couple more questions. 1) should in E=(hw/2)*(n+1/2), shouldn't h be h^2? as p = -ihd/dx and you squared it? My textbook says its just "h" too, so i'm a bit confused there. 2) Do we set m=1 for any case? is it because we consider it to be normalized? why do we not bring the mass term back?
One more thing I found is that all the other references say a+ and a- have ip and -ip terms instead of iwx and -iwx. What difference does this make? and which one is the correct form?
At around 11 , the math shows the ground state of the (spring and mass) harmonic oscillator to be 1/2 (omega) (h) . But what actually is the physical meaning of the ground state of the spring and mass system ?
Thanks for a great video. The frequent clips in this video gives leaves few things unexplained. The clip at 22:17 states that H=½√(2w)a√(2w)a+w/2 =w(aa)+w/2. Shouldn't this be = √(w/2)(aa)+w/2?
Great series. Thanks! I have a question: around 5:40 into this video you replaced (d/dx)^2 with d^2/dx^2. I tried to work it out for ψ = e^((-ω x^2)/2) and I got (d/dx)^2 = ω^2 x^2 but d^2/dx^2 = -ω + ω^2 x^2. Not sure how to reconcile. Did I miss something?? Thanks.
Ashraf Amrou I got stuck on this point too. Squaring a derivative is not the same as taking the second derivative, although the similarity of the notation makes the apparent mistake easy to make.
Drphysicsa sir , question please what is the geometric meaning of stochastic calculus the geometric meaning of ordinary calculus tan the angle between x-axis and the tangent line to the point this for derivative and the area under the curve this is for integration ???
Drphysicsa is one of the best physics teachers in the world. If you don't get it from him, its gonna take a lot of grinding from another person for you to get it right.
Lol I also took the same exam. By the way how did you go? I actually found the time too short! I actually have a very slow brain, take a lot of time to calculate, analyse and arrange things. Only missed answering two short questions :-( Other than that it was not bad. After taking the SM358 I realised quantum mechanics is not actually the hardest course at all as popularly believed. In my opinion the hardest course will be the S345 'physical chemistry'.
Sir, I just want to ask what should I watch first QM playlist or Particle Physics. I also want to thank you for all the knowledge and information you gave us. you make me more curious and curious about the universe and that's the best thing your sharing to us. Curiosity is the enzyme and in a way your a hormone haha. I follow all your videos I hope you make more physics videos, like the implications of physics concepts and more fun Physics videos.
How is it that you're just able to remove h-bar and put it back in later? Is that even mathematically valid? If I wanted to write out a complete explanation and solution to the quantum harmonic oscillator would it be mathematically safe to use this method you've used here? If you'd kept the hbar^2 in there throughout you'd have -ℏ^2/2 instead of -1/2 at the front of the hamiltonian at 11:40. How would you go from this step WITH the hbar^2 to the final E=hbar x omega / 2 ??
Hi Five-Sigma, with regards to being able to remove the hbar and put it back in later, this is perfectly valid and in fact used extensively in physics. Remember that h bar is a constant, so it is just like leaving out any other constant unitl the end. For example, when you integrate you can take any constants out and integrate your function, then multiply byt the constant again, or you can integrate the function multiplied by the constant from the beginning. As to your other questions, it may help to look at this: en.wikipedia.org/wiki/Planck_units
best instruction on line. Perhaps cause there is no stupid camera person, doing continuous facial shots. When will the rest of academia learn from you?
How do you go from p^2+(wx)^2 to (p+iwx)(p-iwx) when x and p are not commutative? Are we taking x as a position variable, then changing it back to an operator?
great upload but we MUST listen to audio simulation of that types for example a sign gives a permanent annoying sound and the harmonic oscilator a more realistic sound, also some types produce types of noise, not sertain solution - but this is called a noise genetator. with harmonic osicillating and noise modular transistors, we can make a cheap quantum computer with no extracold parts. also already in keyboards we have some quantum mechanical harmonic oscilators and modular noises, but most mathematicians sound engineers and transistor producers are racists among each other simple because we need higher iqs to support each other like a team. Nature is one, the universe is unintelligible if we create walls
Thanks for kind comments. The maths is a good fit to what actually happens but doesn't of course explain why it does. As I tried to explain at the beginning of the series the only justification I can offer for the way the maths turns out is because it works.
Dr.PhysicsA, first, thanks for this great video. I would like to point out that there could be a possible mistake at 8:44 in the video. You are missing a 'x' after the 2 (after performing differentiation). However, you continue with more 2x later. Please tell me if I'm wrong. I do not understand this part.
Thank you so much again for these videos, they're the highlight of my week and I can't wait for the particle physics to follow. Some quick questions/feedback. I can follow the math fine, but often you don't explain why you're doing something and I get lost. E.g., at 17:11, what's the rationale for taking the commutator there? At 20:30, I got a division by zero for that commutator. Why can we use a+ and a- as operators? Finally, I don't understand what the outcome has to do with oscillations.
Another superb "lecture". DrPhysicsA has a unique ability to explain complex concepts in physics/maths in an easily comprehensible manner. All his videos are excellent and also most interesting. Thank you.
Dear Dr. Physics, This is a great series and I will be watching the next round. There was one typo on I forget which QM video (one or two back) where you moved from discrete to integral case but left one of two terms as f(j) versus f(x). Will try to find it. What I really like about this series is that in a pretty short time one gets a strong sense of the mode of thought and type of calculations involved. Quick question if I may: it it poss. to derive the usual statement of uncertainty as prod. of variances from the one in your video? Thanks and hope to see more (and more advanced topics too). YJ
I would like to second the opinion of the reviewer below that said "Simply brilliant series of lectures!". Its great. Thank you very much for this. The downside is that its finished. Cant you continue with more QM concepts series?
Wonderful series of lectures. Helped build understandings that I simply did not grasp some 30 years ago. Good way to spend a day and a half. Thank you...
Hi Keneu. Omega is equal to sqrt(k/m) because that's the value of omega that's necessary to solve the Schrodinger equation for the harmonic oscillator. We have a potential energy function of [ V(x) = 1/2 k x^2 ] in our Hamiltonian operator. Once we solve [ H psi(x) = E psi(x) ] the solution shows that [ E_n = 1/2 hbar omega ], where n is a non-negative integer (0, 1, 2, ...) and omega is sqrt(k/m). This also makes omega match up with the classical harmonic oscillator angular frequency as well.
