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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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Theory that we cannot observe everything

If I remember physics class correctly, and if not feel free to correct me, there is a theory that shows that we can not observe everything. I think the example given was energy and space. So either we ...
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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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Are operator matrices of $x$ and $p$ the same for all systems?

I recently read Computing quantum eigenvalues made easy . In that article, the author used the position and momentum operator's matrix form in terms of the normalized eigenstates of a harmonic ...
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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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Average values of $\langle n|x_{op}|n\rangle$ and $\langle n|p_{op}|n\rangle$ [closed]

Let an harmonic oscillator described by the hamiltonian $H=p^2/2m+(1/2)mw^2x^2$. I have determined that the average values of the observables $x$ and $p$ in energy eigenstates , $\langle n|x|n\rangle$ ...
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What is the magnitude of a tensor property in a fixed direction?

If I have a physical property represented by a $3 \times 3$ tensor, how can I find its magnitude in a particular direction, say $(\phi, \theta)$ in spherical coordinate system?
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Why don't expectation values for a stationary state evolve over time?

I have an observable $O$ with operator $\hat{O}$. $\Psi_1$ is a wave function in an energy eigenstate, and $\psi_1$ is the corresponding spatial wave function. $E$ is the corresponding energy. It is ...
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How to understand observables in quantum field theory

I am reading a paper about quantum field theory, something that I am new to. I have some experience with quantum mechanics. In the paper, it explains how a field is a function from a spacetime ...
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Determining the state of a system

My textbook says: "To determine the state of a system at a given instant, it suffices to perform on the system a set of measurements corresponding to a complete set of commuting observables (CSCO)" ...
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Heisenberg uncertainty principle in daily life

I need some examples of the Heisenberg uncertainty principle on a basic level, or if possible in daily life. Or maybe a simple explanation for validity of the principle in easier words. I cannot get ...
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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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What is the implication of overlap between eigenstates of two operators in Quantum Mechanics?

For instance, what does it mean that a certain position eigenstate is also an energy eigenstate? I understand that measurable (Observables) in Quantum mechanics are the operators. Their eigenvalues ...
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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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Why are entanglement and purity non-linear functions of $\rho$?

Any linear function of the density matrix can be related to a proper observable, but is it not the case of entanglement and purity?
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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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Do we or do we not observe (measure) superpositions all the time?

This is not a duplicate, the other answers do not specifically solve the contradiction, nor do they give an exact answer. I have read this question: Are we so sure about superposition? How do we ...
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Why must momentum operator in infinite well be self adjoint?

First, let me preface this statement by saying I know that there exists no (unique) self adjoint extension of the standard differential operator for the space $L_2([0,1])$. However, when one attempts ...
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Eigenvalues of Unitary Matrices

I am considering the standard equation for a unitary transformation $\alpha^* = U \alpha U^{-1}$, where $\alpha$ is an arbitrary linear operator and $U$ is a unitary matrix. Since in quantum ...
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What precisely must you provide to specify the Hilbert space for a particular system in quantum mechanics?

We have: $$i\hbar\frac{d |\Psi(t)\rangle}{d t} = H|\Psi(t)\rangle$$ $|\Psi\rangle$ is an element of the Hilbert space. However, the Hilbert space is unspecified. As an analogy, in classical ...
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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 ....
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Do observables only amount to computing functions of outcome probabilities?

It is well known that in quantum mechanics any Hermitian operator $A$ can be thought of as an observable. Given any (pure) state $\lvert\psi\rangle$, measuring such observable gives an average ...
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Is there a physical observable with the same units as $c/G$?

Dividing the speed of light $c$ by the gravitational constant $G$ yields the dimension mass*time/area or mass/(length * speed) Is there a physical quantity used in textbooks with this dimension? I ...
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Is there a difference between a Hermitian operator and an observable?

My poorly written lecture notes say that any Hermitian operator does have a complete set of orthogonal eigenstates with real corresponding eigenvalues and is therefore an observable. In the article ...
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Why is an operator the quantum mechanical analogue of an observable?

I used to think because that, if objects are treated as waves, then using operators is the necessary thing to do in order to "retrieve" the observable from a given wavefunction. For example, in ...
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Observing the conserved canonical momenta

Suppose I have a Lagrangian $\mathcal{L}[\phi]$ with $\phi$ a cyclic variable, which means that the Lagrangian is symmetric under shift of $\phi\rightarrow\phi+c\quad$. The equation of motion will be ...
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Quantum mechanics on operator [closed]

If any operator is commute with Hamilton then they are labelled such a way that the energy eigenstate are equal and we also know it is a constant of motion. I don't related constant of motion with ...
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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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Are $\hat x$ and $\hat p$ assumed to be time-independent operators?

In the book Quantum Mechanics by Cohen-Tannoudji, at $G_{III}$, it is given that and then in the comment section, it is also given that so I'm pretty confused in here, because in one side, they say ...
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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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is there a way to experimentally determine the mean of $\hat A$, namely $\langle \hat A \rangle$?

Let $A$ be an observable, then, is there a way to experimentally determine the mean of $\hat A$, namely $\langle \hat A \rangle$? I mean, for example, consider the position operator; it is ...
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Is the identity operator correspond to the observable which states the existence of system?

As it is claimed in this question, the identity operator is an hermitian operator, but not an observable. However, if I were to build a device, which only measures the existence of an electron in a ...
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Is there any intuitive reason behind why should the eigenfunctions of observables form a basis for our Hilbert space?

Is there any intuitive reason behind why should the eigenfunctions of observables form a basis for our Hilbert space ? For example, in the case of Stern-Gerlach experiment, sending the beam that has ...
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Is is possible to have a pair commuting observables only in a single direction?

In quantum mechanics, for two observables to be compatible, successive measurements of the observables, say $A$ and $B$, should yield the same result as earlier, i.e if we do the measurements with the ...
Say I have the following operator: \hat { L } =\hbar { \sum_{ \sigma ,l,p } { l } \int_{ 0 }^{ \infty }\!{ \mathrm{d}{ k }_{ 0 }\,\hat { { { a }}}_{ \sigma ,l,p }^{ \dagger } } } \left({ k }_{...