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Is it possible to construct density matrix for a discrete system like a lattice ? For example i have a 1D half filled lattice with 10 sites, half filled means each site has just 1 electron. I have constructed the Hamiltonian matrix using all the possible combinations of basis states. Then i have diagonalized the matrix to get e.values and e.states. now how to proceed for density matrix, reduced density matrix and entanglement entropy?

Does this series contain all videos?

It is the most succinct introduction to Noether's theorem I've ever seen online. Your lectures are almost comparable to Lenoard Susskind's Classical mechanics series, except you go deeper with more elaborations on the derivations of the formulations. Many thanks for the excellent work !

Where are you dear prof ? After watching your lectures on condensed matter physics I got motivated to do PhD in the same subject. So kindly put more videos so that i can educate myself for the betterment.

V great thanks

❤From pakistan

Thanks a lot! That helps me solve my recent problems!

Dark magic. Makes no sense at all, but at the same time in the end you see it kind of makes sense to introduce all these structures, they're pretty and give rise to all the other laws from such a simple and basic concept.

ruclips.net/video/M7A7_s3cX8g/видео.html

Hi Dr. Mitchell, are the lectures on Classical Mechanics gone from the site ? Thanks

why at 1:25:25 you use 1*3 matrix instead of 1*2

Hello Dr Mitchell, I hope this message finds you well. I believe you have unlisted these videos. It might be hard to find them again in the future. Can you make them permanent again? Thank you and I am glad for these lectures.

Thank you for the lecture professor, So, both methods (Equation of Motion and Layman’s representation) don’t work with interacting particles. But how do theorists calculate the spectral functions like XAS and XPS for very complicated materials? Is it done using cumulant Green functions or something else? My question might not be well-formed, but I'm completely new to this field. and if there any materials can help a beginner's like me I will appreciate. Thank you for considering my question.

This idea of breaking down wave propagation in free space as multiple-slit diffraction but increasing the number of barriers and slits is really great!

Very nice lecture! Thank you!!

Very interesting subject

I'm certain that anything in the universe comes into being from interference. All phenomena seem to slide through the rifts of spacetime left untouched by other phenomena.

Fist time i have understood something…its mind blowing just like Feynman.Thanks❤❤❤❤

One of the most elegant topics in QM and QFT.

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adagommala

Excellent! I can only echo the other comments. You are an excellent teacher! More lectures please!

The Barn Door Paradox The setting out of the barn door paradox (14:40) would be a lot simpler starting with the back doors of the barns on the right and left halves of the diagram closed at the start, as in the previous hand drawn sequence, and remaining closed until the front of the ladder gets there. At this point the back door snaps open. At that same time the front door on the left half of the diagram snaps shut. The one on the right half has to wait until the ladder has cleared before shutting. Each door then only undergoes one event (opening for the back door and shutting for the front one). At 19:00 you clearly explain that the fallacy in the apparent paradox is the assumption that the two barn doors both move in tandem in the two frames. In fact, an observer on the ladder does not see the two barn door moves as simultaneous. The back door move is first and the front door follows. However, at 26:00 you don't close the loop by spelling out that in the primed (ladder) frame of reference the two door events occur at different times. You focus instead on the length of the ladder, which is the source of people's confusion. In the ladder frame the back door move is the rightmost red dot. The front door move is an event at the intersection of the left blue vertical with the x'=0 axis, which is some time later (if I understand this correctly, which is by no means a given). This is why the ladder gets through without mishap. A couple of other points on this sequence: 1. It is not clear why the black x=ct line is there. Presumably it is explained in an earlier lecture, and might have something to do with how the x' (i.e. ct'= 0 line) is drawn. 2. At 24:05, it is not obvious why B is shorter than Bo as it is clearly longer on the diagram. Presumably, the length units of x and x' must be different. i.e. 1 metre on the x' axis is not the same length on this diagram as 1 metre on x. Thanks for the video. It certainly got me thinking. Whether along the right lines or not I will leave to others.

In the first example, I don't understand how that is the only curve that satisfies the boundary conditions... wouldn't the ball also be at O and T if it didn't move, just sat there for the time it would take to go up and come back down? I am confused because (I think?) the derivation explicitly left out the starting force. I understand why if it is moving it has to follow that curve in order to land precisely at time T given the constant g. I don't understand how we derive from just the boundary conditions + Newton's laws that any movement took place....

This is the best you can get, really enjoy all your lectures

I’ve been loving your channel since I came across it recently. Keep up the good work. One note: The armchair physicists in the comments of your videos are almost as entertaining as the videos. They are theoretical physicists, because their physics degrees are theoretical 😂

Phenomenal lecture, if there was just one change I would have loved you to have explained where the minus sign came from in the four vector

Could anyone shed some light on how to prove [H, S^2tot] = 0 and [H, S^ztot] = 0 at the end of the video? We can see it is indeed this case in the 2 spin system, because we can express H in terms of S^2tot. And We know [S^ztot, S^2tot] = 0, so they all commute. But here we cannot explicitly express the Hamiltonian, how can I see it? Thanks for your help in advance.

Thank you!!

Brilliant.

Excellent and ground up explanation of Feynman path integral. Thank you.

Dude gets more jacked with each video!

Dear Dr. Mitchell, I solved the Q 2.1Charged planes problem using images method. Calculating the electric field from two pontual charges (the real one and its image) in a generic point on the conductor plane and then obtaining the electrical densitiy vector is possible to get the expression for the surface charge distribution directly without any derivatives. But by using this method I got a slightly different result from yours ( my denominator is 2 pi instead of only pi). Would you mind to check if something is wrong? By the way your classes are excelent and I would like to ask you for a good reference to perform computational physics (I intend to make animations of electrical charge moving under different electric/magnetic field)? Thanks in advance, Marcio.

Brilliant explanation! Thank you!

Great video! Very well explained thanks Dr Mitchell!

Brilliant stuff thumbs up

Gravity doesnt exist just lies. Its all about mass and fall of bodies..

In the two pulleys example, it seems like the second pulley (the lower one) becomes an accelerated frame of reference when the mass m1 is accelerating. Do we need to account for that by changing the value of g for the second pulley to g plus the second time derivative of q1?

Does finding U matrices mean we are actually figuring out clebsch gordan coefficients?

14:10 Principle of Least Action

So good!!!

Love from turkeyy

Very good, very useful, very clear. I love it. Thank you so much

Best course ever! Thank you!

Great video! Probably the best explanation I have ever seen of these ideas. I have one (perhaps stupid) question: If the paths around the path of least action creates constructive interference, why can't paths around (very near) other paths do the same? In your example you drew 3 vectors whose sum was nearly zero, and therefore had destructive interference, but would one not see constructive interference for vectors near (similar) any of the individual paths in that example? So I guess I don't understand why the sum of these vectors _around_ the path of least action is so special, given the argument about the sum of the vectors in your example.

This lecture would improve a lot IMHO if the speaker focused on the concept of "action" before stating the Lagrangian. Explain what is going on with all the trajectories, what is the problem mathematically. As it is action remains something arbitrary and mystical, while the Lagrangian pops up "deos ex machina" of sorts.

Absolutely great work sir

The paradoxes are actual contradictions that indicate that the principle of relativity is false. The Einstein mathematics is faulty and produces mathematical contradictions that can not be removed. So his theory is actually invalid as shown by these real unresolvable paradoxes.

Thats great prof....you are a real teacher...❤❤❤❤

At around 8.40 you draw the Density of states of an uniform 1D chain. Is it correct ??? I say this because for an infinite 1D lattice you get Van Hove singularity at the band edges, which I believe in 1D is non-integrable. If I take a tight-binding 1D lattice with nearest neighbour hopping, these singularities will occur at -2t and 2t, where t is the hopping parameter.