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Another question regards the following: U are explaining the description of a field in a box with the boundary condition saying that it disappears on the box walls. It is obvious, that only some wafe-lenghts are allowed here, which U may call quanta. But is a free field without any box quantized too ?

Nice explanation, but why do U have an both expenents =/- i(kr - wt) ? If time increases r increases too, so both parts are running forward. Is't it neccessary to put one exponent (kr + wt) to have one part running backwords ?

Is this applicable to antennas in telecommunications? I believe this is mostly for research applications with phd or doctorate level. Just curious but very well explained.subs and liked🎉🎉

simple and easy to follow :)

Hey. Are you sure about the signs in the (Euclidean) Lagrangian? Most texts have a relative negative sign between the two terms, i.e. L = - ( + <n|∂/∂τ|n> - <n|H|n> ). I was also following your derivation, and I feel that the error might have crept in at the timestamp 22:19, where you approximate <n_{j+1}|n_{j}>. The way I calculate it is as follows - |n_{j+1}> = |n_{τ+ε}> = |n_τ> + ε . ∂/∂τ|n_τ> => <n_{j}|n_{j+1}> = <n_τ | n_τ> + ε . <n_τ | ∂/∂τ |n_τ> = 1 "+" ε <n_τ | (∂/∂τ |n_τ>) And ofcourse, we need to take a complex conjugate to get <n_{j+1}|n_{j}>, which only switches the state on which the derivative acts <n_{j + 1} | n_{j}> = 1 "+" ε <∂/∂τ n_τ |n_τ> The highlighted "+" above seems to be the source of discrepancy to me.

리만 아티야 내쉬는 리만가설을 풀었다.

There is a type of Space-Time diagram in which the scale for both systems is the same. They are called "Loedel Palumbo Diagrams" and with them any analysis of special relativity is significantly simpler. They were developed in the mid-20th century by the Uruguayan physicist Enrique Loedel Palumbo from the simple, but brilliant idea, of considering in a diagram of Minkowski not one, but two "mobile" systems with the same speed, but in opposite directions and then remove the "fixed" system from the middle and... voila! you have two systems with the same scale! .The relative speed between these two systems is now given by the sine of the angle between the axes, not by the tangetic and trigonometry is that of all life. It is a shame that they are not very widespread.The deduction is very simple and can be found in the following link ruclips.net/video/o4kKeG8PyyM/видео.html

How can you use a non-relavistic gauge when an electromagnetic wave always travels at the speed of light. All Maxwell Equations are inherently Lorentz invariants. Indeed that is the actual original derivation of Lorentz transforms before Einstein other way in 1905.

I really appreciate your knowledge sharing and more impressed with your educational background. It gives me confidence to study at the OU and took a master's at renowned university.

Hi!Can you please elaborate on the taylor expansion?

If you upload future videos it would be useful to do small edits where mistakes are made as you did in a prior video for a missing prefactor. I wasted a few minutes working out the calculations myself several times and error-checking urs, but a few minutes later in the video you do so anyway so it was a bit of a waste of my time feeling crazy I had made an error. I've gone through this content several times over the last 5 years and I've gotten tripped out and seen others tripped up in these integrals including Kardar himself so I think it is quite common for us to make these slight housekeeping errors when manipulating these more tricky integrals.

how did you find the alpha = -2beta?

Superb video, was very helpful!!!

Nice video!

Great explanation

I believe you have defined the creation and annihilation operators incorrectly. Taking your expression for a at 39:10 and substituting in the expressions for q and p into the expression for a, I find that the final result has an additional factor of hbar. I believe that the hbar should be on the denominator in the fracrtion for the expression for the creation and annihilation operators. My maths is a bit rusty though so it's worth checking.

Nice video! Would it be possible for you to share the whiteboard annotations with me?

why do you not find additive inverse please reply

Excellent. You're vivid and articulate. Like your delivery style very much. I was looking for such a lecture. Thanks dude.

Very nice and useful 👌👍👍👌

Keep going

Sorry if it's a stupid question, but why is there no contribution to E from the scalar potential (-grad V)?

This creates a huge paradox. What if each receiver has a second function. Instead of just turning on, it also disconnects the wiring of the opposite receiver. That would mean create two different alternative realities that cannot coexist. How can the lights be both on in "A's" reality, & 1 off 1 on in "B"s reality???

There are some sort of questions were we need to make assumptions such as u is equal to something and v is equal to something so we can solve it. So, how I can know that I don't need to make assumptions and when I need to ?

Thank you, it was useful for me <3

So for the zero vector and the additive inverse we have to find a value within the set to make the axiom true and if there is none, the set is not a vector space?

Blessings, good work, join our Week in Review Sunday nights, and hope to do another Science of COnsciousness conference post stream today

Hey I just found your channel looking for linear algebra courses, I was wondering how making RUclips videos has helped you develop your understanding of a subject and if you recommend I persue this learning technique?

I am searching for this type of video for some time, I found this video, at last, it cleared all my doubts thank you

Thanks bro

*👍😉привет от тренера по футболу!*

your a very brave guy

Awesome

Keep up with the work ! I really like physics but ive never really had the chance to study it properly in school. I only know the basics haha I like your videos ! Have a nice day ! :)