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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Sequential Stern-Gerlach devices - realizable experiment or teaching aid?

At least one textbook [1] uses sequential Stern-Gerlach devices to introduce to students that the components of angular momentum are incompatible observables. Viz., the $z$-up beam from a SG device ...
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510 views

Where does a fermionic coherent state live (which Hilbert space)?

There have been a couple of questions on fermionic coherent states, but I didn't find any that covered the following question: If I define a coherent fermionic state in the 2-level-system spanned by $...
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How are local observables encoded in this formulation of quantum field theory as a functor?

I've recently begun trying to understand a formulation of quantum field theory as a functor from a category of spacetimes-with-boundaries (bordisms) to a category of Hilbert spaces, as reviewed in [1]....
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115 views

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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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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255 views

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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2answers
102 views

Can we dispense with the Manifold in General Relativity?

I am studying Quantum Gravity by Rovelli. In chapter 2, the author describes the path that Einstein followed to arrive to General Relativity (GR). At the end of the discussion of the hole argument, ...
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95 views

$C^*$ 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 ...
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84 views

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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1answer
3k views

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 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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30 views

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 ...
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79 views

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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1answer
130 views

Physical significance of the canonical energy-momentum tensor

I have a question regarding the physical significance of the canonical energy momentum tensor $T_\nu ^\mu$ in the context of classical field theory. It is defined as $T_\nu ^\mu = \frac{\partial \...
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1answer
91 views

Observables labelling one-particle states in Quantum Field Theory

I'm studying introductory QFT using the first volume of Weinberg's series, and i'm having problems in understanding how single particle states of the free theory are labelled, i.e. what observables ...
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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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100 views

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 ...
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113 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, ...
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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 ...
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315 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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1answer
389 views

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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197 views

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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124 views

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 ...
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112 views

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.
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Is the parity operator an observable?

I'm trying to justify whether the parity operator is an observable in quantum mechanics, and if so, why. I'm at a loss here, any advice on how to tackle this problem?
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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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1answer
46 views

Density of observable is expected value of Dirac delta

I am currently studying Statistical Mechanics and already have a background in probability and statistics. However, there are still things that remain unclear to me. So far I understand that time ...
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1answer
32 views

Can there exist energy eigenstates that cannot be labelled by the good quantum numbers?

I'm trying to visually understand good quantum numbers for the example Hamiltonian of a composite system $$H = \lambda J_{1}.J_{2}$$ As I understand it, the energy of the system (assuming fixed ...
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Quantum observables in nonstandard Hilbert space

Consider a Hermitian $(n \times n)$-matrix $A$, and a Hilbert space $\mathbb{C}^n$, foreseen with a nonstandard inner product. (An inner product $s(\cdot,\cdot)$ is standard if for any two vectors $x =...
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Heterodyne detector

In which sense an heterodyne detector does not measure an observable? I mean, its POVM is proportional to the projector on coherent states, and the coherent states are an overcomplete set for the ...
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2answers
56 views

Post-measurement $\psi$ in quantum mechanics

I have a question regarding the wave function after a measurement. Everything I found online says that this is the following formula: $\psi = \frac{M_m\psi}{\sqrt{P(m)}}$ Where $P(m)$ is the ...
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Measuring the observable

I am working through this quantum mechanics homework question and I am a little confused on what I am being asked to do. I have come to one of two possible answers but I don't think either is correct. ...
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81 views

What is the intuitivity about C*-Algebras being used as the fundamental objects in physics?

While asking about operators on this site, many answers mentioned "C*-algebras" to be the fundamental mathematical element corresponding to an observable (in QFT and QM at least), and choosing a ...
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Quantum Mechanics “inside out”

Let us assume that we know only some basic QM notions which are part of the Heisenberg picture of quantum mechanics and Dirac quantization Physical observables are represented by Hermitian operators $...
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Good quantum numbers from a given hamiltonian

The primary reason asking this question to understand good quantum number from a giver Hamiltonian. Is there any good approach that we can identify them? For example: We have a square and in that ...
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57 views

Conservation laws and Gauge transformations

I am studying gauge transformations, and my professor asked me: "Can the potentials obtained by the Lorenz gauge be considered physical quantities?" I assumed that "physical quantity" is ...
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107 views

For any two unitarily equivalent observables, can both be measured by the same experimental apparatus?

If we have an observable $A$, and a unitary operator $\hat U$, one can easily show that both $\hat A$ and $\hat U \hat A \hat U^{\dagger}$ have the same spectrum - in fact, they are called unitarily ...
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What is the variance of |S| in Bell's inequality (CHSH inequality)

Sorry that this isn't a quick question but I didn't know how to make it shorter. I am struggling with this for quite a long time and I would appreciate every help that I can get. I could not find a ...
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2answers
74 views

Is the period a physical observable in General Relativity?

I am currently seeing the classical tests of GR. To justify the introduction of a test based on the Doppler effect, the professor says that the previous test ( Shapiro and echo-radar test ) is based ...
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1answer
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Relationship between the Galilei Group and the Phase Space

This question is kind of a follow up question to my last question on the need for canonical commutation relations and conjugate observables. A comment from Valter Moretti suggested that, given a ...
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139 views

Physical quantity related to the parity operator

There is a statement in quantum mechanics that for every physical quantity, there exists a Hermitian operator. The converse is also true. So the question is, what physical quantity is related to the ...
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Can we measure without collapsing (too much) the wave function, according to decoherence theory?

According to decoherence theory, the collapse of the wave function is a continuous process due to interaction with environment. In a measure, there are interactions with photons (for example). Can we ...
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Uncertainty Principle with the corresponding operators

Why does the corresponding operator do not commute if there is uncertainty related to two observables A and B that states $\Delta A\,\Delta B > 0 $ ?
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How to measure $\mathbb{L}^2$ and $L_z $ simultaneously

What does an experiment look like, in which both quantities are measured simultanously?
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“Independent simultaneous eigenbras” in Dirac's book 'Principles of Quantum Mechanics'

I've been puzzling through this book off and on and can usually work out what is going on via other external references on the Intertubes. But, this paragraph from pages 55 and 56 has me a bit ...
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2answers
256 views

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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How does dependence between observables appear?

Consider a double slit interference experiment with particle A. After going through the slits the state is: $\left| \Psi \right\rangle = {\alpha _1}\left| {{a_1}} \right\rangle + {\alpha _2}\left| {...