Quantum operator Definition and 12 Threads

This question is related to equation (1),(3), and (4) in the [paper][1] [1]: https://arxiv.org/abs/2002.12252

Hello guys, I struggle with one step in a calculation to show a quantum operator equality .It would be nice to get some help from you.The problematic step is red marked.I make a photo of my whiteboard activities.The main problem is the step where two infinite sums pops although I work...

Summary:: Linear Quantum harmonic oscillator and expectation value of the potential energy (time dependent) Hello, I have attached a picture of the full question, but I am stuck on part b). I have found the expectation value of the <momentum> and the <total energy> However I am struggling with...

Homework Statement Using [x,eiap]=-ħaeiap show that xneiap = eiap(x-ħa)n Homework Equations [x,eiap]=-ħaeiap From which it follows that, xeiap = eiap(x-ħa) The Attempt at a Solution [xn,eiap] = [xxn-1,eiap] = [x,eiap]xn-1 + x[xn-1,eiap]...

Hi! I want to know under what conditions the operator expectation values of a product of operators can be expressed as a product of their individual expectation values. Specifically, under what conditions does the following relation hold for quantum operators (For my specific purpose, these are...

Assume ##\varPsi## is an arbitrary quantum state, and ##\hat{O}## is an arbitrary quantum operator, can the expectation $$\int\varPsi^{*}\hat{O}\varPsi$$ be imaginary?

Consider the operator Ô, choose a convenient base and obtain the representation of \ exp{(iÔ)} Ô = \bigl(\begin{smallmatrix} 1 & \sqrt{3} \\ \sqrt{3} & -1 \end{smallmatrix}\bigr) Attempt at solution: So, i read on Cohen-Tannjoudji's Q.M. book that if the matrix is diagonal you can just...

Homework Statement Spin Operator S has eigenvectors |R> and |L>, S|R> = |R> S|L> =-|L> eigenvectors are orthonormal Homework Equations Operator A is Hermitian if <ψ|A|Θ> = <Θ|A|ψ>* The Attempt at a Solution <ψ|S|L> = <L|S|ψ>* // Has to be true if S is Hermitian LHS...

Hi all! I was reviewing some basic quantum mechanics, and I was trying to 'derive' the equation -i \hbar \frac{\partial}{\partial x} \psi_{(t,x)} = <x| \hat{P} | \psi > using the commutator relation, and the form of the identity operator. OK, I know that the proper, mathematical way to prove the...

Is there a "magnitude of momentum" quantum operator? Homework Statement Is the ground state of the infinite square well an eigenfunction of momentum? If so, what is its momentum? If not, why not? What can you say about the magnitude of the momentum? Homework Equations Ground state...

Hallo, I was wondering what is the physical significance of scalar field \Phi (x) as an quantum operator. \Phi (x) have canonical commutation relation such as [ \Phi (x) , \pi (x) ] so it must be an opertor, thus what are his eigenstates? Thanks, Omri

Homework Statement I got stuck to this problem: To prove that (x p)^2 is not equal to (x)^2 (p)^2 where x and p are position and mometum operator in QM. Homework Equations The Attempt at a Solution I approached this way: Two operators A and B are equal iff Af=Bf for all f...