Variational Principle Introduction

In this video, I introduce the variational principle in quantum mechanics, how it is derived, and why you might want to use it.
Hope you found this video helpful, please post in the comments below anything I can do to improve future videos, or suggestions you have for future videos. This video was made possible by my Patrons, and I'd like to give a big shout-out to MoonWook Oh.

[@zacharythatcher7328]

Wow. Such an amazing explanation! As a material scientist that is desperately trying to understand enough physics to work on synchrotrons and quantum materials, you are a lifesaver.

[@captainhd9741]

I read the words literally with a full-stop in the thumbnail “Give up.” well I tell myself that pretty often in question practice

[@JordanEdmundsEECS]

💯

[@subhakantasahoo9760]

When there problem in understand 😉physics I always thinks in mind jordan bro is there to make everything simple😀

[@JordanEdmundsEECS]

;)

[@RakeshKumar-nu8yn]

You make it so simple enjoyed learning 😊

[@user-ni7zi1jd3g]

Very very nice

[@canyadigit6274]

8:54 maybe I’m not understanding correctly, but you’ve defined the “guess” energy to be the eigenvalue corresponding to the guess wave function which is a superposition of the energy eigenstates. However, superpositions of eigenstates tend to not correspond to a single energy eigenvalue (unless the energy spectra is degenerate). Is this wrong?

[@Johnny-tz2dx]

Hey! I think i get your question so the response I have is that you can think of the guess energy has the summation of all the unique eigenvalues of the superposition of energy eigenstates

[@SkanderTALEBHACINE]

best regards from Algeria, when optimizing the parameter value could we get the exact E1 value and for what conditions yes or no? thanks again

[@JordanEdmundsEECS]

Hello from the U.S. :D Nope, because no matter how good our guess is we still have the wrong wavefunction. It will always be larger unless you happened to guess exactly the correct functional form.

[@SkanderTALEBHACINE]

@@JordanEdmundsEECS So how could we estimate our relative uncertainty over energy? are we far away? or are we sufficiently near the true unknown value? thanks again

[@JordanEdmundsEECS]

We have no idea 🤷‍♀️ You can use other approximate methods (such as perturbation theory) to get another estimate (I thiiink this can give you a lower bound but I’m not certain).

[@SkanderTALEBHACINE]

@@JordanEdmundsEECS thanks again

[@nazmurrahmannobel11]

But,sir if the guessed wavefunction belong to same Hilbert space where the true wavefunction exists we can use the expansion postulate (superposition of eignstates) to prove the inequality on your video .This matter motivates me to believe cannot guess any function.But I have seen many books were I don't seen any restrictions for guessing function.Can anyone help me?

[@infinity-and-regards]

How do you know our guessed wavefunction is an eigenstate of the Hamiltian? Do we choose it to be like that?

[@JordanEdmundsEECS]

The whole point is that it doesn’t have to be - it’s just the further away it is from the true eigenstate the further away our energy will be from the actual ground state energy.

[@infinity-and-regards]

@@JordanEdmundsEECS Thanks for your response! What I don't understand is that you equate H psi = E psi while we don't know if it's an eigenstate or not. What am I missing? Cheers

[@JordanEdmundsEECS]

Ah, that's just writing down the time-independent S.E. We know it's going to be true for *some* set of states, we just don't know what those states are. So we expand our 'test' wavefunction in terms of those (hypothetical and unknown) states.

[@thomasknoll7643]

@@JordanEdmundsEECS Hi. Thank you for this great video! There is one point which I didn't understand. How can we in practice expand a guess wavefunction in terms of functions that we actually don't know? Isn't that the whole point? In other words: How do we know that the functions Wochenende use to expand the guess wavefunction are actually these true (hypothetical and unknown) states?

[@milanrai3607]

if you have true wavefunctions, why are you guessing and for what??

[@milanrai3607]

7:54

[@jenajej147]

We give up 😂

[@taylormoskalyk4483]

"Blah blah blah blah blah..."