Відео

Dm me on telegram tch1001 I’ll send u the pdf

glad it helped! sorry what timestamp is the last step? it's been a long time since i uploaded this

@@tanchienhao oh yes, let’s say 25:30 where the loop interval was converted to the solid angle

​@@TheFirstSpeaker Ah, i see, differential solid angle d\Omega = \sin \theta d\theta d\phi for a 2D subsurface of the sphere, assume first it encloses \theta=0. then the 2D integral \int\int d\Omega can be done by first evaluating the d\theta integral \int_0^2\pi d\phi \int_0^\theta(\phi) d\theta \sin\theta = \int_0^2\pi d\phi [-\cos\theta]^\theta(\phi)_0 = \int_0^2\pi d\phi 1 - \cos\theta\phi this is the result seen in 17:14 if the - was changed to a +, \int_0^2\pi d\phi 1 + \cos\theta\phi = \int_0^2\pi d\phi 2 - (1 - \cos\theta\phi) = 4\pi - solid angle which is the result in 25:30 the case where the subsurface does not enclose the \theta=0 point can be thought of as the difference between 2 loops that do

@@tanchienhao I see! Then /int (1-cos\theta)d]phi = \int sin\theta d\theta d\phi = \int d\omega

@@tanchienhao Thank you!

the fourier transform of dirac delta is the constant function

glad it helped! you from nus?

@@tanchienhao Yes!! I guess you saw my Source Academy videos? 😁

@@TheWildStatistician yep! how’d you come across this hahaha, you do competitive programming?

@@tanchienhao Yes! I just finished CS2040S and I am reading Prof. Steven Halim's CP4 :)!

Yes

@@tanchienhao Sir first of all thank you for replying 🙏 kindly tell one more thing , I was studying the Green's function for 3D Helmholtz equation....is this same as Fourier transform method of constructing the green's function? I mean are these the same topic?

@@QuarkRiti1729 Fourier transform is a general technique to find the Green's function of linear differential operators, so yep they are related

@@tanchienhao gotcha..thank you ✨

Glad u liked it! I hvnt done any experiments myself but you can probably find these info in existing papers on EPM

Thank you!! Glad it helped

Thanks! Can you contact me on telegram (tch1001) I’ll drop you the pdf there

glad you found it helpful! thanks

Thanks!!! Glad it helped

I have given talks on special relativity and thermodynamics, the videos are on this channel (search SPOT)

I have given talks on special relativity and thermodynamics, the videos are on this channel (search SPOT)

Thanks!

Sir at the end you obtain berry phase for an electron in a magnetic field (parameter space)(time varying) describing importance of Bloch sphere but what is its application please reply! thanku@@tanchienhao

@@md.zafaralam if you perform interferometry with electrons (eg double slit) but with a magnetic field, the fringes will shift according to the magnetic field strengths along the 2 paths. Also for condensed matter parameter space is crystal momentum and that leads to topological insulators!

Thanku sir for clearing my doubt💖@@tanchienhao

this is a presentation for the Singapore national team training

@@tanchienhao for what discipline/competition?

@@ES-qe1nh ipho

​@@tanchienhao Interesting! Seems at best tangentially related to ipho type questions

Thank you! Let me know what topics you want to see next

​@@tanchienhaorotation

@@Cooososoo okay!

Glad you liked it!

at 4:56, Sx = 1/2(S_+ + S_-) and Sy = 1/(2i) (S_+ - S_-). (equation 23 and 24) and S_+ and S_i are given in terms of a,a+,b,b+ (equation 26 and 27) then using the fact that commutator is bilinear, i.e. [a+b, c+d] = [a,c] + [b,c] + [a,d] + [b,d] we can calculate [Sx, Sy]

It’s at 00:00

​@@tanchienhaohow can I copy those links

I got a $300 mic alr hahaha is the audio bad :( I wasted my money I guess

I’ve been regularly uploading hahahaha but it’s just educational videos

The hopping energy from one site to the next, which is the expectation value of the Hamiltonian sandwiched between a bra state with an electron at site x and a ket state with an electron at site x+1

thanks for the idea! if you want to discuss phys olym / need help you can drop me a text on telegram (tch1001)

Asboth a short course on topological insulators

I took a look and it seems to be a numerical way to calculate berry curvature of real systems? I am not an expert yet, but I don’t mind discussing it. You can contact me on telegram at tch1001

Thanks!

Thanks! Here it is ua-cam.com/video/GFZ3Asw4dc4/v-deo.html and ua-cam.com/video/cNggTPVUciA/v-deo.html

Thanks for the kind words! I got a better microphone so hopefully for new videos it’ll sound better :)

It’s on my todo list!

@@tanchienhao Thanks bro can you please upload ASAP its a request

@@vinvvinv7460 I will try my best!

I substituted the previous line Fourier expansion of G into (nabla^2 - a^2) G, The inverted triangle (nabla) is replaced with ik

@@tanchienhao thanks for the answer. Why is it replaced with ik and not just k? Thanks again!

I am asking because I have to do the same problem but with (i * o3 * d/dt - w) where o3 is a pauli matrix.

@@armbrusl because the Fourier transform of f(x) to f(k) = integral of exp(ikx) f(x) dx uses ikx instead of kx

@@armbrusl it could be useful if you send me the full question on telegram @tch1001 and I can help you there

The calculations done in this video are gross simplifications of actual atoms, and are only meant for pedagogical/theoretical analysis, you may be keen in looking for Density functional theory simulations for physical systems :) hope that helps

@@tanchienhao Thank you. Actually i was thinking if this analytical TB approach can work if there is more than one type of atom inside the unit cell.

@@deepmondal323 yeah it can! like the last example in this video has two sites within one unit cell. sometimes they are called sublattice index.

Great! I’ll get working on it but I do have a lot on my hands at the moment haha