Variational Principle Introduction 

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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.

@@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

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).

@@JordanEdmundsEECS thanks again

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

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.

@@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

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.

@@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?