Hermitian operators in quantum mechanics

📚 Hermitian operators represent physical quantities in quantum mechanics. We first show that their eigenvalues, which give the possible outcomes of the measurement of a physical quantity, are always real numbers. Second, we show that their eigenstates, which tell us about the probability of obtaining a particular outcome for a measurement, form a basis of state space, so they can be used to represent any physical state.

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Director and writer: BM
Producer and designer: MC

[ryanjbuchanan]

"The eigenstate of a Hermitian operator corresponding to different Hermitian operators are orthogonal." Wow. 4 years at MIT and you just explained what all of my professors couldn't.

[Dudenobody]

Awesome video! Thank you for explaining this, I was struggling to understand it.

[shutupimlearning]

very concise explanation, glad i found this channel

[MrVsoral]

I have come across some videos on Quantum simulations where it was mentioned that any Hermitian operator (a Hamiltonian) can be expressed as a linear sum of Identity and Pauli Matrices. For example:

H = a₁₂ σ₁ⓧσ₂ + a₁₃ σ₁ⓧσ₃ + a₂₃ σ₂ⓧσ₃ + ... + a₀₁ Iⓧσ₁ + ...

where a₁₂ ... a₀₁ .. are scalars.
However I am unable to find any details on this; specifically any proof or algorithm to decompose a Hermitian matrix in above form.

Do you have a video that explains this, or can you please refer me to an literature that explains this ab-initio?
Thanks in advance.

[tejareddy]

The explanation is very clear and precise. I am unable to catch the speed and watching it at 0.75x. But no problem.

[TheWingEmpire]

Thank You very much, it was really clarifying! :)

[floribus]

Sorry when I missed it. Is there a video that proves the existence if eigenvalues/vectors in the first place?
Your videos are great, very clear!

[BruinChang]

I remember there are s, p, d, f orbitals taught in general chemistry. Does the "degenerate" eigen-values relate to the p, d, f orbitals? Because a single eigen-value maps to multiple eigen-states, and the one-to-many mapping reminds me about diverse orbitals.

[sibongumusaws]

where can I learn the bra-ket notation, beginner friendly and advance to more complex stuff like this. Any recommendations

[kaushikgupta]

for gram Schmidt normalization of more than 2 eigenstates, We have to apply the perpendicular conditions for all eigenstates separately, right?

[progra_kun]

Hola, no me queda claro, lambda es un real porque, de ser imaginario, la igualdad no podría darse, cierto? Lo digo porque se asume que lambda estrella es de por sí, un complejo conjugado, imagino que es por eso que nos dicen que no trabajaremos con el término imaginario, cierto?

[nomanahmadkhan]

Another brilliant video indeed. I am a bit confused about "n" (as in i=1, 2, 3, n, ) and "N" (as in N-dimensional space). Are these same/different? Can these be same/different?

[jumpyalexa]

Thank you so much, you may actually be better than Griffiths! Side note, you have a lovely voice!

[anoopmis.pandey]

At time 07:00 and earlier as well, you have mentioned for orthonormal bases the scalar product is delta ij, but shouldn't it be zero for both are different and 1 if both are same like <1|1>=1 and <1|0> = 0?

[marticircunsiduxans]

Hi professor! I think that there's a mistake in 4:43. The eigenvalue resulting from the operation of the bra phi with the operator A should be a conjugate. Am I right?

[KaranveerSingh-xntv]

Is every entry of hermitian matrix a real number?

[syahrilsabtu]

Hi prof. how to Prove that the operators for position
x and momentum P are Hermitian. can you make this video.

[joeaverage]

Will you guys make videos on scattering?

[wdobni]

what part of a proton is 'observable'? has anybody ever 'observed' an electron?

[mohankurra]

Hi sir, I have a small doubt
Is hermitian and Hamiltonian operators are same are different plz explain sir