Expectation value of Hermitian operators

[@Leonugent2012]

This professor is brilliant!

[@demr04]

Very interesting that the eigenvalues are the expected value of the observable. There is not better combo between linear álgebra and probability theory.

[@ricardocesargomes7274]

Excellent Lectures!

[@MultiChantal22]

Hi is the expectation value itself ( ) an operator ?? I am very confused I got a text book problem to prove that if operator A is Hermitian than prove that A - is also Hermitian ... How are you supposed to subtract an expectation value from its operator 😭

[@BBonBon]

Hey, did you manage to find an answer?

[@chrisr9320]

The expectation value of an operator is the result of a definite integral, so it's a number. A - is an operator if it means A - 1 with 1 being the identity operator. It is also Hermitian bc the 1 operator is Hermitian an is real.

[@demr04]

Expectation value is an operator of a set. In previous lecture he explain that given a distribution with respect to an observable, you define the expected value of the observable as the acting of the operator (associated with the observable) in the inner product of the common wave-function. So, when he speaks about the expected value of an operator, he refers to it, as of an observable. Given that the expected value of an observable it's a real scalar, is invariant under transposition and complex conjugation. If you sustrate the expected value to an hermitian operator and applied the dagger operator, obviously remains the same.

[@cafe-tomate]

Expectation value of Q expressed in the Φ space is also real

[@not_amanullah]

Thanks ❤️🤍

[@AMITSHARMA-cy8oj]

Of Most importance.

[@not_amanullah]

This is helpful ❤️🤍

[@AdarshKumar-dq5wy]

something wrong with sound

[@mitocw]

The sound was recorded with the built-in camera microphone so you hear more room noise, lecturer's voice is not as loud and clear. You are used to sound from a wireless lavalier microphone attached to the lecture's clothing... which is used for most of our videos unless something goes wrong (not enough time to setup / dead batteries / signal interference / etc.).

[@clivemakongo]

@@mitocw this for free so I'm not shedding tears about it lol, thanks for what you guys do.

[@parasmittal3697]

@@mitocw to hell with poor sound , this is saving me in exams .

[@Physics_PhD]

any reason why not use dirac notationie bra and kets !!!

[@sorooshsaghebi9465]

he just skipped the Dirac notation part, the Dirac notations literally translate to what he wrote, we don't use the Dirac notations either in our quantum course (I am a bachelor chem student)

[@MdShakil-rl4yk]

good

[@jesseeagleman5271]

All about pumping up M.I.T. its the best

[@hasanrahman2778]

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