Quantum Chemistry 4.7 - Hermitian Operators

Short lecture Hermitian operators in quantum mechanics.

Measured values of physical properties in quantum mechanics must correspond to eigenvalues of their quantum operators. Physical properties have real number values, thus the eigenvalues of these operators must always be real. Hermitian operators are guaranteed to produce real eigenvalues, as defined here for eigenfunctions and general functions. Every operator in quantum mechanics is required to be a Hermitian operator.

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[vishakhajayasekera]

Thank you so much for making these videos. I took quantum chemistry lectures for 2 years now. And i just started the advanced course and im glad these videos are there. They've helped me a looottt :-D Thank you once again

[aleyoung]

I️ am taking Quantum Chem now in college, I️ am so glad these videos are available. Very helpful.

[anniejoe]

Thank you so much! I'm finally starting to understand what we've been talking about in my Theoretical Chemistry lectures :D
Great video!

[TheLegendO]

Thank you so much for taking the time to make all of these videos!

[ayasaki.pb_]

In the last step, why are you naming fn and fm in the reverse order? if you named them from the beginning, the integrand should became f*m A fn = fm A* fn*

[nkyu]

hello^^ let me ask you about taking a complex conjugate of.
1. (exp(a+bi))* = exp(a-bi) ? Or (exp(a+bi))* = (c+di)* = c-di ?
2. when taking a complex conjugate of AΨ=aΨ,
I think it should be (AΨ)*=(aΨ)*. and maybe (aΨ)* can be a(Ψ)* or a*Ψ* because 'a' is a real number. but how does it end up being A*Ψ*=aΨ* ?

[michaelmichon]

If <m|A|n> = (a_n)<m|n> = a_n, and (<n|A|m>)* = (a_m)*<m|n> = a_m, does a_n need to equal a_m for <A> = <A>* ? And if |m> =/= |n>, does <m|n> still equal 1?

[dhoonygo]

Quick question : Measured properties are not necessarily real, in that case, unlikely to be Hermitian operator?

[nkyu]

in this video you didn't cover why Hermitain operator also works for general functions, right?

[oskarmarelja]

is <A*> the same as <A>* ? thank you