# What is Quantum operator: Definition and 12 Discussions

In physics, an operator is a function over a space of physical states onto another space of physical states. The simplest example of the utility of operators is the study of symmetry (which makes the concept of a group useful in this context). Because of this, they are very useful tools in classical mechanics. Operators are even more important in quantum mechanics, where they form an intrinsic part of the formulation of the theory.

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1. ### A Relation between the density matrix and the annihilation operator

This question is related to equation (1),(3), and (4) in the [paper][1] [1]: https://arxiv.org/abs/2002.12252
2. ### I Struggling with one step to show quantum operator equality

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...
3. ### QHO: Time dependant expectation value of the potential energy

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...
4. ### Expanding the original commutator on the LHS

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]...
5. ### A Independence of Operator expectation values

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...
6. ### I Can the expectation of an operator be imaginary?

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?
7. ### Exponentiating Matrices: Representation of \exp{(iÔ)}

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...
8. ### Quantum operator hermiticity. Show that S is Hermitian

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...
9. ### Quantum Operator Derivation: Exploring Intuitive Approaches

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...
10. ### Is there a magnitude of momentum quantum operator?

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...
11. ### Scalar field as quantum operator.

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
12. ### How can I prove that (x p)^2 is not equal to (x)^2 (p)^2 in quantum mechanics?

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...