# Questions tagged [operators]

In physics, an operator is almost always either a square matrix or a linear mapping between two function spaces (defined on, say, $\mathbb R^n$). Operators serve as observables and as time evolution operators in Quantum Mechanics. This tag will most often find valid use in quantum mechanics; don't use this tag just because your equations contain "everyday operations" like $\times$, $+$!

3,945 questions
Filter by
Sorted by
Tagged with
17 views

### Can I define $\hat{x}$ as $x\delta(x'-x)$?

Operators can be thought of as matrices. Since matrices have two indices and involve summing: $A^i_j \psi^j\equiv A^i_0\psi^0 + A^i_1\psi^1 + A^i_2\psi^2 \dots$ and a summation between 2 vectors turns ...
1 vote
53 views

### Thinking of a linear operator as a (1,1) tensor

I am reading that a linear operator $A$ can be thought of as a (1,1) tensor [where $(r,s)$ corresponds to $r$ vectors and $s$ dual vectors]. This can be done by saying $$A(v,f) \equiv f(Av)$$ where $v$...
25 views

### Relation between diagonal and off-diagonal entries of Hermitian Operator

I am started doing a project in Quantum Chemistry and stumbled upon a problem which I can not seem to find the answer to. As the title suggests, I am looking for a relation between the diagonal and ...
1 vote
50 views

### $(a - a^t)e^{\frac{1}{2} a^ta^t} | 0 \rangle = 0$ [closed]

When talking about the limits of squeezed states, we reach the conclusion that $e^{\frac{1}{2} a^ta^t} | 0 \rangle$ must be an eigenstate for momentum since the uncertainty in momentum becomes zero. ...
58 views

### Rigorously building a Fock space, creation/annihilation operators and inner products in a QFT

I would like to understand how one can install a set of states, starting with a vacuum, define creation/annihilation operators for the vacuum, solve for mode functions and define inner products in a ...
170 views

42 views

942 views

### Confusion regarding Heisenberg Uncertainty Principle

I've been studying some Quantum Mechanics recently. I am a mathematics student but I've always been interested in physics so I am currently learning this material from a more mathematical treatment of ...
52 views

### What is the angular momentum operator? [closed]

On one hand, since the angular momentum is: $$L^{ij} = r^i p^j - r^j p^i$$ so it makes sense for the angular momentum operator to be: $$\hat{L}^{ij}= -i\hbar (r^i \partial^j - r^j \partial^i)$$ On the ...
22 views

### State Vector and Density matrix [duplicate]

I have a slight confusion with the two. From what I have understood, state vector describes pure states, which means that with a probability $1$, our state is going to be in that state. However, if ...
137 views

### Is $\mathcal{L}^{*}_{L}(\rho) = 0$ $\forall$ $\rho$ $\in\{\rho: \langle\mathcal{L}_{L}(V)\rangle_{\rho}= 0\}$ true?

[Context: I have observed the fact, $\mathcal{L}^{*}_{L}(\rho) = 0$ $\forall$ $\rho$ $\in\{\rho: \langle\mathcal{L}_{L}(V)\rangle_{\rho}= 0\}$ (meaning of the symbols are below) true numerically, ...
1 vote
40 views

### Commutation relation between squares of angular momentum [duplicate]

We usually come across the formula $$\vec{L}.\vec{S}=\frac{1}{2}\left[\vec{J}^2-\vec{L}^2-\vec{S}^2\right].$$ Do $\vec{J}^2$, $\vec{L}^2$ and $\vec{S}^2$ commute always, or do they commute under ...
81 views

40 views

### In what way are eigenfunctions of an observable operator complete? [duplicate]

I am a physics undergraduate reading through Griffiths's 2ed Quantum book. In section 3.4 (Generalized Statistical Interpretation), Griffiths states: The eigenfunctions of an observable operator are ...
63 views

### Srednicki's QFT: Why $\langle p|\phi(0)|0\rangle$ in the interacting theory is Lorentz invariant?

I am reading Srednicki's QFT and I have met a problem. In its section 5, (5.18) , after deducing the LSZ formula, in order to check whether his supposition "that the creation operators of free ...
39 views

### When does an operator in Quantum Mechanics have a discrete spectrum? [duplicate]

Say one has a classical Hamiltonian system with generalised coordinates $q$ and conjugate momenta $p$. After canonical quantization, promoting them to operators $\hat{q}, \hat{p}$, how can one ...
122 views

$[x, \hat{H}]$ or $[\hat{p}, \hat{H}]$ can be computed by substituting $\frac{\hat{p}^2}{2m} + V(x)$ for $\hat{H}$ and doing some simple calculations. e.g $$[x, \hat{H}] = [x, \frac{\hat{p}^2}{2m} + V(... 2 votes 1 answer 42 views ### Worldsheet constraint Bosonic String I am currently studying David Tong's notes on String theory and there’s a step taken in writing out the worldsheet constraint in lightcone coordinates \sigma^{\pm} for the closed string that I’m not ... 1 vote 1 answer 55 views ### Why is there only one eigenket per eigenvalue of the number operator? [duplicate] Let's "define" (I put quotes since it's not a definition, but just requiring a property) the operator a such that:$$[a,a^\dagger]=1$$then$$n=a^\dagger a$$No other assumptions are made ... 0 votes 1 answer 54 views ### Why does the interaction hamiltonian not commute with itself at different times? If you have a poincare invariant Hamiltonian H, then the Hamiltonian must commute with itself at different times and not explicitly depend on time. If the Hamiltonian H can be written as H = H_{... -2 votes 1 answer 38 views ### Relation of two commuting operators to other operators Consider two commuting quantum operators:$$\hat{A} \hat{B} = \hat{B} \hat{A} \quad $$For any operator \hat{C} , how can we prove that:$$\hat{A} \hat{C} \hat{B} \hat{C} = \hat{B} \hat{C} \hat{A} \...
(Original title: is time-odering operator a linear operator?) I'm confused with two formulas, one of which is  \mathcal{T} \exp \left [-\frac{\mathrm{i}}{\hbar} \int_{t_0}^t \mathrm{d} t' \hat{H}_I(...