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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Domain space of compatible and incompatible operators (observables)

Sakurai (Modern Quantum Mechanics, by J.J. Sakurai) states in the section on compatible operators: Let us first consider the case of compatible observables A and B. As usual, we assume that the ket ...
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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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Can GR be reformulated in terms of invariant observables?

Question So recently I was thinking about this: How many scalars are available in $4$ dimensions in General Relativity (without being redundant)? For example, with metric we can construct the ...
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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 is the physical meaning of the sum of two non-commuting observables?

Scenario: ${\mathcal A}$ and ${\mathcal B}$ are two observables. Mathematically we model them by two Hermitian operators $A\colon H \to H$ and $B\colon H \to H$ on a separable Hilbert space. ...
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Does the wave function of a particle collapse if info about an observable is available in seperate chunks for many observers?

To start, I just started learning QM today so... keep that in mind. What I was trying to say is: suppose (for example) there is a box with a subatomic particle in it, the box is a 3D space so we plot ...
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Simultaneous measurements in Quantum Mechanics

In the notes I am using, it states that if two observables A and B are measured simultaneously, then the measurement of A does not affect the measurement of B, and vice versa. However, why does the ...
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Where does the postulate of quantum mechanic that possible results are eigenvalues come from? [duplicate]

Where does the idea come from, that possible results of quantum measurement are eigenvalues of the operator corresponding to the observable?
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Tracing out an observable vs integrating over unitaries

Let $O$ be an observable on a Hilbert space $\mathcal{H}$, and let $B$ be a subset of the spins composing $\mathcal{H}$, and let $\bar{B}$ be its complement. Now define $$\displaystyle O_B = \frac{1}{...
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What methods do we use to measure position/momentum of quantum systems in the lab?

I've seen this question asked before but couldn't find a satisfactory answer. What is the difference between measuring position vs. momentum in the lab? Is it just something to do with the energy of ...
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Trying to understand spin in quantum mechanics

I'm trying to understand the concept of spin in Quantum Mechanics. I'm reading "Road to Reality" by Penrose, which despite not being a textbook, is reputed to give one a deep insight into physical ...
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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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Prove conservation law in quantum mechanics

I major in Math, and I am studying Quantum Mechanics (QM). I see the conservation law in QM as a mathematical theorem. Please check if my understanding is right, and help me to prove the theorem? ...
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Eigenstate of field operator in QFT

Why don't people discuss the eigenstate of the field operator? For example, the real scalar field the field operator is Hermitian, so its eigenstate is an observable quantity.
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Intuitive meaning of Hilbert Space formalism

I am totally confused about the Hilbert Space formalism of Quantum Mechanics. Can somebody please elaborate on the following points: The observables are given by self-adjoint operators on the ...
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Eigenvalues, Hermitian operators and observables in quantum mechanics

Consider a hermitian operator. So a) in a space of infinite dimension its eigenvectors are a base. b) in a finite-dimensional space the matrix that represents the hermitian operator is always ...
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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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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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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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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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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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Is energy $E$ in Schrödinger equation an observable/ Can $E$ be measured?

Take this quantum approach to estimate mean energy of a molecule: $$\langle\psi|H|\psi\rangle=\overline E$$ Question: Is $E$ an observable? How we can compare it to an experimental value? i.e how ...
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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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How does non-commutativity lead to uncertainty?

I read that the non-commutativity of the quantum operators leads to the uncertainty principle. What I don't understand is how both things hang together. Is it that when you measure one thing first ...
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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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What is the Momentum Operator?

I know the equation for the momentum operator, but what exactly is the momentum operator? It's bizarre to me that taking the derivative of the wave function, which is an operator, should return ...
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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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Do imaginary measurements exists? [duplicate]

I'm sorry if this question is too metaphysical, but I will give it a try. My textbook in introductory quantum mechanics is basing a lot of its proof and derivations on the fact that the value of the ...
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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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How does one actually measure the position or momentum of a quantum object?

How is the position or momentum of a Quantum particle is measured experimentally in laboratory? Suppose we want to know the position or momentum of quantum particle which is kept in a box i.e. an ...
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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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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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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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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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Why do we use Hermitian operators in QM?

Position, momentum, energy and other observables yield real-valued measurements. The Hilbert-space formalism accounts for this physical fact by associating observables with Hermitian ('self-adjoint') ...
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What does it mean for 2 observables to be compatible?

If I have 2 observable operators $A$ and $B$, if $A$ and $B$ commute: $[A, B] = 0$, then they must necessarily form a complete set of commuting observables (CSCO). Essentially, if 2 observables are ...
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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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Commutativity vs Compatibility

As far as I know, two compatible observables have a complete set of common eigenvectors, and using this fact, one can prove that their corresponding operators are commutative. Well now is the converse ...
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How to think of matrices as observables?

I'm reading Nielsen and Chuang. In one of the early chapters, they introduce some matrices such as $$X = \begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}.$$ They interperet this as a gate that ...
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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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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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Is the probability current an observable?

Is the probability current in Quantum Mechanics an observable? If so, how can it me measured (directly or indirectly)?
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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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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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Is the wave function objective or subjective?

Here is a question I am curious about. Is the wave function objective or subjective, or is such a question meaningless? Conventionally, subjectivity is as follows: if a quantity is subjective then ...
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Why hermitian, after all? [duplicate]

This question is going to look a lot like a duplicate, but I've read dozens of related posts and they don't touch the subject. Here we go. Why are observables represented by hermitian operators? ...