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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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Is there a physical significance to non-normal states of the algebra of observables?

Quantum theory may be formalized in several different ways. Generally, the physical discussion of different states of a quantum system distinguishes pure and mixed states, and then subsumes both in a ...
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The sum of two observables: Can its interpretation depend on more than just those two observables?

In the context of quantum theory, suppose we have two models $M_1$ and $M_2$ formulated on the same Hilbert space. Suppose that the operator $A$ is an observable in both models, with the "same" ...
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Measurement formalisms - POVM formalism vs Hermitian observables

I am thinking in following way of thinking about measurements in quantum mechanics. Please correct any false statements I may be making below. We start with POVMs. Let our POVM be a set of positive ...
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Measuring the Dirac field

If the Dirac field $\psi(x)$ is to the electron as the Electromagnetic field is to the photon, why is it that we can measure the Electromagnetic field, whereas the Dirac field we cannot?
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Observables and local observations in quantum field theory

I have recently taken a quantum field theory course at my university but it focused heavily on the mathematics of the theory and not the physics. So I am left with a few questions on observables and ...
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What is the set of observables of a quantum system?

This is a question I am wondering about because the answer to it seems to have some interesting - but perhaps already long considered and dismissed because it's been settled - implications for the ...
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Breakdown of quantum mechanical observables in cosmology

In several different contexts, I've heard the claim that quantum gravity in an accelerating universe messes with our ability to define precise quantum observables.* One version of the argument goes ...
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Observables that encode all the information in a wavefunction

Let's consider the position space representation of the single particle Hilbert space and for simplicity let's stick to one dimension: $L^2(\mathbb{R})$. Let's say a collection of observables $O_1,...,...
Physical Mathematics's user avatar
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How to define an observable on a subsystem?

Suppose we have a bipartite system $AB$. I would intuitively say that an observable $O$ "acts as the identity on $A$" if $$ O=\mathbb 1_A \otimes O_B$$ But then I would also say this if $$ \...
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What does the operator's explicit dependence or independence on time actually mean in Quantum mechanics?

Consider the equation of motion for the expectation value of an operator $A$ $$\frac{d\langle A\rangle}{dt} = \frac{1}{i\hbar}\langle [A,H]\rangle + \left \langle \frac{\partial A}{\partial t} \right \...
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$C^*$ algebra of observables for a particle in a ring

It is known that for a free particle in $\mathbb{R}$, the $C^*$ algebra of the observables is given by the Heisenberg algebra i.e. generated by $p,q$ such that $[q,p]= i$ ($h=1$). For technical ...
Overflowian's user avatar
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Fields: Fundamental and Physical, yet Unobservable?

I'm currently working through Robert Klauber's Student Friendly Quantum Field Theory, which by the way is much more accessible than other texts like, say, Peskin and Schroeder, for others also coming ...
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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?
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Nearly degenerate observable in quantum mechanics

An observable in quantum mechanics is represented by a hermitian matrix. When an observation is made the state collapses to one of the eigenstates of the matrix. What happens if some eigenvalues are ...
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Do bubble/vacuum diagrams have some physical implication?

While calculating S-matrix elements $$\langle\Omega|T \{ \phi(x_1)...\phi(x_n) \}|\Omega\rangle=\frac{\langle0|T \Big\{ \phi_0(x_1)...\phi_0(x_n) e^{i\int d^4x\mathcal{L}_{i}[\phi_0]}\Big\}|0\rangle}{\...
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What is the Hamiltonian of this number theoretic system?

Background Let us have the following orthonormal basis such that: $$ \langle m | n \rangle = \delta_{mn}$$ Consider the following operators defined as: $$ \hat 1 = | 1 \rangle \langle 1 | + | 2 \...
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Is the vanishing commutator of observables outside the light cone only a necessary or also a sufficient condition for causality?

The equal-time commutator of observables in QFT has to vanish outside the light cone in order to ensure causality. Mathematically spoken, $[ \bar{\psi}(x)\Gamma_1\psi(x),\bar{\psi}(y)\Gamma_2\psi(y)]|...
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Expectation value of a ladder operator

I am going back over old Q.M simple harmonic motion material and, as I can't see an answer on the web, I would like to confirm the validity of an assumption. Using the ladder operators: $$ {\...
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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 ...
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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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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 ...
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On completeness of a set of commuting operators for homonuclear diatomic molecules

The electronic Hamiltonian for a homonuclear diatomic molecule is $$\hat{H}=-\sum_{i=1}^N \frac{\hbar^2}{2m} \nabla^2_i -\sum_{i=1}^N \frac{Z_Ae^2}{4\pi\epsilon_0|\vec{r}_i-\vec{R}_A|} -\sum_{i=1}^N \...
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Does spin entanglement imply position entanglement?

My question is whether two electrons can be entangled only with respect to their spins but not with respect to some other observable, such as position. I initially believed that spin-entanglement ...
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Derivation of the Heisenberg EOM in the most general case

I'm currently reading chapter 2.2 of Sakurai where the Heisenberg picture is detailed. However, in the text Sakurai doesn't treat the most general case of a time-dependent hamiltonian $\mathcal{H}(t)$,...
jediparth's user avatar
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Confusion regarding the interpretation of simultaneity in the uncertainty principle

After studying the derivation of the generalised uncertainty principle, what I understand is: Suppose we have two operators associated with observables $\hat{A}$ and $\hat{B}$. If I prepare a large ...
Pratham Hullamballi's user avatar
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Can local supersymmetry be characterized entirely in terms of observables?

Global symmetries can be defined through their effect on observables. In contrast, quantum theories are often constructed with the help of symmetries that leave observables invariant, like the ...
Chiral Anomaly's user avatar
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What quantities in Schwarzchild spacetime correspond to those we measure?

There are many classical tests of general relativity such as gravitational red shift, motion of particles, etc. In those calculations, we compare the result under general relativity with that under ...
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Does the Kalman filter incorporate a Heisenberg-like uncertainty principle?

In the case of mechanical systems, applying the Kalman filter involves combining model based prediction (using an apriori known dynamical model) with real-world noisy observations of the positions and ...
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Measuring momentum

I'm new here, possibly my apologies for misplacing. After a measurement in quantum mechanics, the wavefunction collapses to an eigenstate corresponding to the outcome of the measurement. Thus if we ...
uncertain's user avatar
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Was the notion of observable really necessary before quantum physics?

I'm a mathematician who's been struggling with the search of connections between physics theories and $C^*$-algebras. The most known connection I found was that the observables in quantum mechanics ...
André Porto's user avatar
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Observables of Dirac equation

So I learned about the Dirac equation which describes a relativistic free particle with spin $\frac{1}{2}$. I get the mathematics but what i can't find nowhere: What are the observables of this ...
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Maximally uncorrelated observables as a consequence of unbiasedness relation

In the case of a fully correlated scenario of $A$ and $B$, which are descirbed in mutually unbiased bases, why do the other observables have to be maximally uncorrelated. How does this follow from the ...
Yalom's user avatar
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What significance do field-operators have, if they don't correspond to observables because of non-hermicity?

Since field-operators are not always hermitian (for example in case of a complex scalar field, or the dirac-field), they don't (in the quantum-mechanical sense) correspond to observables. Does that ...
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How to define an Operator Product Expansion (OPE) on arbitrary Riemann surface for a CFT?

Whenever we define the OPE of a 2D CFT, we do so (at least in the literature that I have come across) on the complex plane. Similarly, the commutation relations between conformal generators $L_n$ and ...
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Quantum Observation

Bear with me if I present a lack of knowledge - QM is not my field. There's a common notion in QM that until a particle is observed (measured), its properties are not definite, but rather are spread ...
Yuval Weissler's user avatar
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143 views

What does "contextuality" mean in the context of partial rather than complete quantum measurements?

The Kochen-Specker theorem is often described as ruling out "noncontextual" classical hidden variable theories. I understand the math behind the theorem, but I'm a little unclear on the exact, ...
tparker's user avatar
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What happens when one "observes' a quantum field, and how do particles get involved?

I've recently begun my journey to understand QFT. I apologize in advance for the length of the post, but there are gaps in my understanding of how I, as an experiementalist, interact with fields to ...
Dragonsheep's user avatar
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411 views

Simultaneous measurement of non-commuting observables without uncertainty

A pair of non-commuting Observables $\hat{X}$ and $\hat{P}$ does not have a common set of eigenfunctions, i.e., it can not be measured simultaneously. Let us for the sake of simplicity assume that $[\...
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Have Witten-type TQFT's nonconservation of energy and momentum in interactions?

Witten-type topological quantum field theories are based on cohomology theories. Every observable must lie in a cohomology class. May be $G$ a geometric field. Then every observable expectation value ...
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1 answer
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Hamiltonian symmetry Lie algebra

What is the connection between complete set of commuting observables and generators of the Lie group? I have a Hamiltonian written down in second quantized formalism and I also checked that it ...
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What are you studying when you study a Harmonic Oscillator in QM?

This probably is a naive question - so please forgive a self-studier. In the text I am studying, one builds a HO by placing a particle in a potential that increases quadratically from the origin. The ...
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What is a continuous superselection sector?

I'm studying the terrible subject of continuous superselection rules and I faced with the following problem. Usually (continuous or discrete) superselection rules are defined involving a direct ...
moppio89's user avatar
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How does linearity of a measurement imply that the commutator of all measured observables are $c$-numbers?

I really don't understand with the linearity conditions I have where this comes from.
user32462's user avatar
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1 answer
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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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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} \,...
TomS's user avatar
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1 answer
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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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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, $$\...
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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
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Is really hermiticity necessary to be a physical observable? What about larger class of operators like PT invariant operators or pseudo hermitian one?

It's really necessary for an observable represented by an operator acting in a Hilbert space to be hermitian? It's known that not only hermitian operators have real eigenvalues and that also normal ...
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Is wave function measurable?

I apologize for the length of this naive question. I am not sure it is appropriate for this community. Is wave function measurable? This is really a question in Atomic and Molecular Optics. I hear ...
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