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Questions tagged [observables]

A quantum observable is a measurable operator whose corresponding property of the state can be determined by some sequence of physical operations ("observation"), such as submitting the system to various electromagnetic fields and eventually reading a value. In systems governed by classical mechanics, any experimentally observable value can be shown to be given by a real-valued function on the set of all possible system states.

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How is Zig-zag Motion Observable in Quantum Mechanics Given Wave Function Collapse?

I'm puzzled by a concept I read about in a physics text concerning quantum measurement. The text describes the potential to observe a "zig-zag" motion if one could capture images of an ...
CuriousMind's user avatar
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What is the interpretation of the covariance of two quantum observables?

I have been studying the covariance matrix in continuous variable quantum systems and I am struggling to understand the interpretation of this object. In statistics the covariance measures the joint ...
Hermitian_hermit's user avatar
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If an electron is inside an atom, does the expected value of spin measurements also depend on the orbital wavefunction?

The total quantum state of an electron in an atom can be written as the product of the orbital wavefunction and a spinor representing its spin state, $\Psi = \psi(r,\theta,\phi) \otimes \chi$. Say you ...
agaminon's user avatar
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Is Number Operator a Generalized Momentum?

In superconducting circuit, the number operator, $\hat{n}$, and phase operator, $\hat{\varphi}$ are conjugate pairs. Is $\hat{n}$ the canonical momentum, conjugate momentum, and also generalized ...
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Wavefunction with determinate momentum

In page 100 Griffiths' Introduction to Quantum Mechanics, Griffiths states that the eigenvector of $\hat{p}$ in the position basis is $\frac{1}{\sqrt {2\pi\hbar}}e^{\frac{ipx}{\hbar}}$ and states that ...
xyz1234's user avatar
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Closed expression for expected values of $\hat{p}\,\,^{2j}$ for the vacuum state

I am wondering if there is a closed expression for the expected value $\left<0\lvert \hat{p}\,\,^{2j}\lvert 0\right>$ with $j\in\mathbb{N}$, where $\left|0\right>$ is the vacuum state of the ...
Camilo160's user avatar
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Probability for a quantum many particle system of temperature $T$ to be found at temperature $T'$

Suppose we have a system of $N$ particles (let's postpone the question re statistics) in thermal equilibrium, described via a density operator $$ \rho_\beta = Z^{-1} e^{-\beta H} $$ $$ Z = \text{tr} \,...
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How can $L_x$ be an observable?

I'm working with the orbital angular momentum operator $L_x$, and I don't quite understand how it can represent an observable. Using ladder operators, I can write $L_x$ as: $$L_x=\frac{1}{2}(L_++L_-)$$...
Lagrangiano's user avatar
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Is Torsion Observable?

Are there, have there been, or could there be any experiments that might detect any torsion in our corner of the universe? Any results? Or is torsion an unobservable?
Ric's user avatar
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On the choice of observables in linear response theory

For linear response theory I need two observables. The idea is to see how the change in one observable changes the other under weak perturbations in equilibrium state. Suppose I want to see the change ...
Rafi Ullah's user avatar
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What is the Taylor series of the expectation value of an observable in quantum mechanics? [closed]

I recently came across a form of the expectation value of an observable, but a Taylor series (I think?) was taken up to second-order: \begin{equation} \langle O\rangle = \langle O\rangle_{C=0} + \...
NikNack's user avatar
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Is the annihilation operator an observable (it is non-Hermitian)?

In most treatments of quantum mechanics that I have seen, observables of a quantum system are defined using Hermitian operators. The most intuitive reason for this is that Hermitian operators have ...
Biophysman's user avatar
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Why can't we measure different properties of an electron in accordance with its frequency?

sorry if this is a stupid question but its my first one.. Why cant we just observe and electron in accordance to its frequency. Like during one frequency peak we could observe position, next could be ...
omgcchheeessee's user avatar
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What is the observable for the optical field?

Typically, observables in quantum mechanics are associated with Hermitian operators. However, Glauber argues in 1963 ([1]) that the electric field operator $\hat{\mathbf{E}}(x,t)$ is not the relevant ...
Biophysman's user avatar
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Why does the Pauli objection not disqualify the existence of the position operator?

According to the Pauli objection (see for example here or the answer to this question) there can be no time operator $\hat{T}$ canonically conjugate to the Hamiltonian $\hat{H}$ of a physical system ...
Martin Vaughan's user avatar
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1 answer
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Observation without interaction thought experiment [closed]

Here I am going to talk about a thought experiment that I have thought There is some isolated place in the universe where there is no EM field other than the field created by a moving point charge ...
Physics's user avatar
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Observing a particle [duplicate]

We say that there is uncertainty in position when we observe a particle. But first i want to know in detail about how do we observe a particles position and momentum. Suppose we know that an electron ...
Physics's user avatar
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Dictionary between interpretations of field operators

For now, let $\hat{\phi}(x)$ be a quantization of a classical, real scalar field $\phi(x)$. My understanding is that, for fixed $x$, there are three ways to regard the operator $\hat{\phi}(x)$: The ...
JustLikeNumberTheory's user avatar
2 votes
3 answers
142 views

How to represent the state of this system after the measurement?

This is a question my professor gave us in the test. Consider the spin-$\frac{1}{2}$. Alice measured the system along the $z$ direction, and she observed the outcome as $+1$. After Alice's measurement,...
Kevin027's user avatar
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2 answers
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Why are all observed particles on-shell?

I've been trying to self-learn how to do basic QFT calculations and I'm a little bit confused as to what's considered "an interaction". If I want to model an electron releasing a photon I ...
Opisthokont's user avatar
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Introduction of symmetries in quantum mechanics

The (Italian) book that I am currently reading introduces the topic of symmetries in quantum mechanics in the following way: Let O and O' be two distinct observers and let $A$ and $B$ be two ...
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Showing the Variance of an observable in a determinate state is always zero

I am working through Introduction to Quantum Mechanics by David J. Griffiths, and part 3.2.2 shows that the standard deviation of an obervable, $Q$, is always $0$ but I do not understand the steps ...
cookiecainsy's user avatar
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How to prove that the spin operator commutes with the position operator? [duplicate]

In the lecture notes on Quantum Mechanics I'm reading, the author claims that the position operator $\hat{q}$, the square spin operator $\hat{s}^2$ and the spin operator component $\hat{s}_0$ (in a ...
Andrea's user avatar
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Why reasonable observables are made of an even number of fermion fields?

On Michele Maggiore book on QFT (page 91) is stated, out of nothing, that "observables are made of an even number of fermionic operator" and similar sentences is in Peskin book (page 56). Is ...
Andrea's user avatar
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Is there a physical cause of uncertainty? [closed]

The uncertainty principle is confusing me. Considering this image from the article: Is the particle believed to be physically moving with similar capriciousness in real space; and if so, what ...
jazamm's user avatar
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Questions regarding measurement of a qubit

I am trying to understand the basic concept of observable and state. Say that we have a state $|\psi>=|0>$ which is $(1\ \ \ 0)^T$, we have an observable $\sigma_x= \begin{bmatrix}0&1\\1&...
sett the guy's user avatar
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1 answer
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What kind of physical process would correspond to an operator that doesn’t result in an eigenvalue equation: $ \hat{A}ψ=a ψ$?

I'm studying quantum mechanics and I'm trying to understand the concept of operators. They can be represented in general by the equation: $$ \hat{A}ψ=ψ'. $$ Here the wavefunction is changed to $ψ'$ ...
bananenheld's user avatar
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How to practically check if a Hermitian matrix is an observable?

I get that in QM an observable corresponds to a Hermitian operator. And I also get that not all Hermitian operators will correspond to an observable - with all that $C^*algebra$ stuff. Is there a ...
Kasthuri's user avatar
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1 answer
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Does 2-form curvature $\Omega \in \Omega^2(P,\mathfrak{g})$ represent a physical quantity in gauge theory?

In gauge theory, all measurable physical quantities remain invariant under a gauge transformation. I have always seen that the curvature 2-form $\Omega \in \Omega^2(P,\mathfrak{g})$ associated to a ...
eomp's user avatar
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Why is it essential in quantum mechanics for the eigenvectors of an observable to compose a basis spanning the entire state space?

After going through the questions and answers, I still have a question lingering in my mind. So, an observable is defined as a Hermitian operator whose eigenvectors make up a basis for the state space....
user353399's user avatar
1 vote
0 answers
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Eigenvalues of Hermitian Operators [duplicate]

In quantum mechanics, it's well-known that observables are associated as the eigenvalue of a Hermitian operator. My question is, is the converse also true? i.e. the eigenvalue of a Hermitian operator (...
Jovan Alfian Djaja's user avatar
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References on obtaining experimental observables from band structure

I've recently been watching this lecture series in Condensed Matter physics. We have covered second quantization, used it to obtain the tight-binding model and then studied the band structure of ...
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Observables expressed by the lesser Green's function $\tilde{\mathcal{G}}^{<}(k, E)$

I am reading the paper PRB 106, 035102 (2022). In the supplementary materials, it says, within the Green’s function formalism, the thermal and quantum average of an observable θ is expressed as, $$\...
vcuteym's user avatar
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1 answer
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Equivalence of gauge-invariance and physical observable

This is somewhat philosophical than physics. In gauge theories, it is true (more like the first principle) that \begin{equation} \text{ physical observable } \Rightarrow \text{gauge invariant} \end{...
Keith's user avatar
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3 votes
1 answer
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Counterexample to the observable algebra of a region and its causal completion being the same

I was reading a paper by Ed Witten called "Algebras, Regions and Observers". It can be found here: https://arxiv.org/abs/2303.02837 A major theme is theorems relating the algebra of ...
Andreas Christophilopoulos's user avatar
2 votes
2 answers
95 views

Does compatibility of observables imply a measurement of the second observable is unnecessary?

If two operators $ A $ and $ B $ are compatible then their corresponding operators $ \hat{A} $ and $ \hat{B} $ share a common set of eigenfunctions. The eigenvalue-eigenfunction equation for each ...
tom894's user avatar
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Condition on unitary operator for real eigenstates of Hamiltonian

I'm working with the discrete-time quantum walk in which the evolution is described by the unitary operator - $$U = S(C\otimes I)$$ where $C$ is the coin operator (acts on spin degree of freedom of ...
Young Kindaichi's user avatar
1 vote
0 answers
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Koopman-Von Neumann Classical Mechanics From $C^*$-Algebra Approach?

My main question is the following: Is it possible to derive Koopman-von Neumann (KvN) classical mechanics from the $C^*$-Algebra approach to physics (as described here) similar to how the usual ...
jd27's user avatar
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3 answers
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Doubts regarding Quantum Mechanics [closed]

I recently started with Quantum mechanics from The Principles of Quantum Mechanics by R. Shankar. I have studied Linear Algebra in my course already. I have also studied QM from D. J Griffiths(up to ...
Charu _Bamble's user avatar
-1 votes
1 answer
82 views

What is the physical meaning of self-adjoint operator extension?

What does it mean that there isn't any extension of a certain operator in a given domain? Does it imply that I can't apply that operator in that domain, and so that I can't measure some observables (...
hbar's user avatar
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0 answers
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Algebra of observables in Quantum Mechanics

When reading books about Quantum Mechanics, it is generally stated (in a kind of axiomatic way) that in Quantum Mechanics, the state of the system is represented by a vector in some Hilbert space $H$, ...
Weier's user avatar
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1 answer
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Variance/Standard deviation of an observable on a state that is a linear combination of eigenvectors of that observable

I know that when measuring the standard deviation of an observable the result will be zero if the system is an eigenvector of the observable on which i want to calculate the standard deviation. But ...
AlexM3020's user avatar
12 votes
6 answers
2k views

Why are expectation values of an observable important in QM?

I've been reading that expectation values of an observable is all what we can get and are the key quantities of the theory, but performing the same experiment many times would generate a distribution ...
user536450's user avatar
1 vote
2 answers
141 views

Projection operator onto support of distinct observables

Suppose $P_i$ is the projection operator onto the support of the observable $O_i$ defined on some (say, finite dimensional) Hilbert space. I'm curious as to whether we can define the projection ...
Theoreticalhelp's user avatar
11 votes
7 answers
2k views

Definition of four-velocity: why define it with proper time of the object?

The four-velocity(world-velocty) is defined by : $u^μ=\frac{dx^μ}{dτ}$ ,where $τ$ is the proper time of the object. I don't understand why it's defined with respect to the proper time but not the time ...
user381761's user avatar
9 votes
3 answers
1k views

Dirac's definition of probability in quantum mechanics

I'm currently reading "The principles of quantum mechanics" by Dirac, and I'm having some trouble understanding some of his assumptions, because in the quantum mechanics course I'm following ...
Fede's user avatar
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1 answer
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Variance of Observable in Klein-Gordon field theory

In quantum field theory most observables $A$ do not have a definite value in the ground state (vacuum). For an observable $A$, a reasonable measure of the spread in the ground state is its variance $\...
Orion Pax's user avatar
1 vote
2 answers
302 views

Momentum operator and Space operator

This may be a silly question, but given that the momentum operator (say in the $x$-direction) can be written as $$p_x = -i \hbar \frac{\partial}{\partial x},$$ would it be correct to say that $$p_x^2 ...
Oti's user avatar
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2 answers
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"No local gauge invariant observables in gravity"... Is it a classical or quantum statement?

I have seen different explanations to understand why there are no local gauge invariant observables in gravity. Some of them explain that diffeomorphisms are a gauge symmetry of the theory and thus ...
P. C. Spaniel's user avatar
2 votes
1 answer
619 views

Simultaneity and The Uncertainty Principle

So, the uncertainty principle states that one can not measure momentum and position with accuracy simultaneously. However, we know from relativity that simultaneously is something frame dependent in ...
Caio Cesar's user avatar

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