Hermitian operator Definition and 60 Threads

Homework Statement Since the momentum operator is Hermitian why is this wrong: <psi| (p-hat)^2 |psi> = <psi| p-hat p-hat |psi> = <p-hat psi| p-hat |psi> = (p)^2 where p is the expectation value of the momentum. Homework Equations The Attempt at a Solution

problem based on hermitian operator Homework Statement A is an hermitian operator and as we know the eigenstates a of A with eigenvalues a satisfy A psi a = a psi a. How do we show that lambda psi a (lambda is a non zero complex number) is an eigen state belonging to the same eigen...

Homework Statement WTS \langle \hat{A} \rangle = \langle \hat{A} \rangle^\ast The Attempt at a Solution \langle \hat{A} \rangle^\ast = \left(\int \phi_l^\ast \hat{A} \phi_m dx\right)^\ast=\left(\int (\hat{A}\phi_l)^\ast \phi_m dx\right)^\ast= \int \phi_m^\ast \hat{A}\phi_l dx. So...

Can anybody give me a hint about how can i show that if an operator is linear then it's hermitian conjugate is linear. Thanks for your help from now.

show that if A and B are both Hermitian, AB is Hermitian only if [A,B]=0. where or how do io start?

Hi, I'm doing a Quantum mechanics and one of my question is to determine if \frac{d^2}{dx^2} (a second derivative wrt to x) is a Hermitian Operator or not. An operator is Hermitian if it satisfies the following: \int_{-\infty}^{\infty}\Psi^{*}A\Psi =...

would anyone mind showing me, for example, how to prove that d^2/dx^2 is a hermitian operator? I've tried to work it out from two different books; they both prove that the momentum operator is hermitian, but when i try to apply the same thing to the operator d^2/dx^2 i get lost pretty quick...

First post so please go easy on me, here goes: I have looked over the basic definition of what is a Hermitian operator such as: <f|Qf> = <Qf|f> but I still am unclear what to do with this definition if I am asked prove whether or not i(d/dx) or (d^2)/(dx^2) for example are Hermitian...

Is the second derivative with respect to position a hermitian operator? (i.e. d^2/dx^2)? Can anyone prove it? I don't think it is. Thanks

Is the second derivative with respect to position a hermitian operator? (i.e. d^2/dx^2)? Can anyone prove it? I don't think it is. Thanks