Separation of variables and the Schrodinger equation

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Brant Carlson

Brant Carlson

Күн бұрын

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@S13Slydeways
@S13Slydeways 10 жыл бұрын
WOAH! I wish you where my professor! You explain things so thoroughly it makes so much sense.
@Hunar1997
@Hunar1997 7 жыл бұрын
Neil Volk Our professor gave this as a homework .. this video was my savior
@williamnelson4968
@williamnelson4968 10 жыл бұрын
What an excellent series of minilectures! My probability density curve for grokking QM integrated over all of your videos is equal to one (understanding!) thanks to your insightful presentations.
@matrixate
@matrixate 4 жыл бұрын
I envy your students Dr. Calson. I wish that my University had you in their Physics Department. I've learned so much from just your videos alone.
@iknowthatdubin4877
@iknowthatdubin4877 4 жыл бұрын
Great lecture for self independent learners!
@mikebeard3524
@mikebeard3524 8 жыл бұрын
Thank you for your clear explanations. I think you are a great teacher.
@edisonlin1776
@edisonlin1776 9 жыл бұрын
At around 12:15, you explain that the equation f(t) = g(x) must hold for every t and every x. Could you explain why that must be the case? Thanks!
@faielgila7375
@faielgila7375 3 жыл бұрын
That relationship came from simplifying the original differential equation, so if that equality is false then X(x)•T(t) would not be a solution to the differential equation (Six years ago, hopefully this is still relevant for you 😅)
@pedramnoohi2715
@pedramnoohi2715 3 жыл бұрын
@@faielgila7375 hopefully he hasnt bene stuck on this for 6 years lol
@captainhd9741
@captainhd9741 3 жыл бұрын
@@pedramnoohi2715 or dead
@Oh4Chrissake
@Oh4Chrissake 7 жыл бұрын
Lovely insight into the wave equation being a relationship between acceleration and curvature.
@jozokukavica9814
@jozokukavica9814 6 жыл бұрын
Yeah. That point really is a lovely idea.
@stephanie8764
@stephanie8764 9 жыл бұрын
What a fantastic video!! Thanks a lot!
@alessiajacquard
@alessiajacquard 5 жыл бұрын
I understand many concepts with you :D I wish that you share more videos about undergraduate physics like 'electromagnetic theory' :)
@scitwi9164
@scitwi9164 7 жыл бұрын
25:30 So this is basically an *eigenvalue problem* for the differential operator :J The eigenfunction of the differential operator is the exponential function, and the eigenvalue is -i·E/ℏ, or from de Broglie's equation E = h·f = ℏ·ω → E/ℏ = ω we get that the eigenvalue has a form -i·ω .
@jimdogma1537
@jimdogma1537 11 жыл бұрын
Very cool and insightful video. Looking forward to the rest. Thanks.
@aljosagraovac1918
@aljosagraovac1918 11 жыл бұрын
excellently explained and simplified
@brendansmith670
@brendansmith670 8 жыл бұрын
Amazing videos! Very clear.
@alpineblob
@alpineblob 7 жыл бұрын
I needed this video. Thank you!
@jamieluskin1663
@jamieluskin1663 8 жыл бұрын
this is fantastic and so clear thank you!
@AkshitSharma0
@AkshitSharma0 2 жыл бұрын
Sir you are just amazingg, thank you so much!
@elias19
@elias19 9 жыл бұрын
If the schrodinger equation comes from he classical wave equation, why in the first term in the time dependent schrodinger equation appears the psi function in the first derivative and not in the second derivative form? Hope i make miself clear, im not that good at english. thanks
@scitwi9164
@scitwi9164 7 жыл бұрын
It's because the Schrödinger's equation has been derived by taking the formula for the wave function of a "free particle" (plane wave) and replacing the ω and k with E/ℏ and p/ℏ, and then looking for the time and space derivatives, which are needed for the Hamiltonian. The wave equation is not a Hamiltonian - it expresses the dependence between the curvature in space and the curvature in time of the wave function, which are both second-order derivatives. The Schrödinger's equation, on the other hand, expresses the dependence between the kinetic energy (related to changes in time) and the potential energy (related to changes in space), which are first-order derivatives. There's a nice analogy you can take a look at, regarding harmonic motion: The equation for the Simple Harmonic Oscillator (SHO) i s d²x/dt² = -ω²·x, so it is has a second-order derivative, and the solution is that nice sinusoidal oscillation you're probably well familiar with. But the harmonic oscillator can be also expressed in the Hamiltonian way, in terms of energies: the total energy E consists of kinetic energy m·v²/2 and potential energy k·x²/2, so the Hamiltonian is E = m·v²/2 + k·x²/2. Now you can replace the `v` in this formula by the first derivative of position with respect to time, dx/dt, obtaining: E = m·(dx/dt)²/2 + k·x²/2 It is just a different way to express the conditions on the function which describes the motion of the oscillator: one is in terms of curvatures, the other is in terms of energies. But the solution is the same for both, because they both describe the same harmonic oscillator.
@m.huzaifam.siddique8016
@m.huzaifam.siddique8016 6 жыл бұрын
thanks. You are a good teacher
@armelivanbado2046
@armelivanbado2046 5 жыл бұрын
You are the best!
@abdulwilliamgokul2486
@abdulwilliamgokul2486 Жыл бұрын
Excellent sir
@ILsupereroe67
@ILsupereroe67 2 жыл бұрын
At 24:36 how do you know E is real and not complex?
@Andrew6James
@Andrew6James 5 жыл бұрын
Can someone explain why both solutions to the 2nd Order ODE was not included. Should we not get the solution T = Aexp[-sqroot(a)t] + Bexp[sqroot(a)t]? Why has the negative one been ignored?
@tis_i_sana
@tis_i_sana 2 жыл бұрын
No! The ODE has been solved by rearranging the variables and integrating, it is not a seond order ODE with the general solution of Aexp[-wt] + Bexp[wt]
@moussamancer801
@moussamancer801 4 жыл бұрын
hi mister and for the solution of the shrodinger equation in polar cordinates by separation of variables ?
@mohammedtalibmosa7344
@mohammedtalibmosa7344 8 жыл бұрын
thank you so much sir
@sunnypala9694
@sunnypala9694 6 жыл бұрын
Sr great explaination
@scitwi9164
@scitwi9164 7 жыл бұрын
Hmm so what is it that makes an equation separable? How can we tell if a given equation can be solved by separation of variables or not before actually trying? (since the separation process can be messy sometimes, and it would be cool if we could tell if it will work before going into all those gory details :q )
@alcoll1038
@alcoll1038 7 жыл бұрын
Sci Twi I've been wondering myself. From what I can gather (also from the book), if there is another function in the PDE that makes it so that the variables can't be seperated easily, solving the PDE will become a whole lot harder. The example they gave was if V was V(x,t) instead of just V(x), then it will not be possible to solve with SOV if V's variables aren't seperable​ themselves...? I don't know. Maybe there exists some weird PDE that has has the exact opposite property.
@debasishraychawdhuri
@debasishraychawdhuri 3 жыл бұрын
Can V depend on time? Can solve the equation then?
@Blackline60
@Blackline60 7 жыл бұрын
Perfect
@wienerdogplague9643
@wienerdogplague9643 4 жыл бұрын
Jesus Christ is God.
@hrkalita159
@hrkalita159 3 жыл бұрын
*\0(*_*)0/* ᕦ(ಠ_ಠ)ᕤ😡🥴😤
@aleksanderasimov4899
@aleksanderasimov4899 3 жыл бұрын
fuck yeah baby
@Maxwell_Integral
@Maxwell_Integral Ай бұрын
Amen brother
@Hunar1997
@Hunar1997 7 жыл бұрын
Thank you very very much
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