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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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 (...
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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 $H$, ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 $\...
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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 ...
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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 ...
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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 ...
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How does the state operator relate to the complete set of basis vectors?
I quantum mechanics we can represent the state of a system $\vert\psi\rangle$ in some Hilbert space as a complete set of basis vectors $\vert n\rangle$;
\begin{equation}
\vert\psi\rangle=\sum_n^Nc_n\...
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Proving Non-degenerateness for Compatible observables [closed]
Hi everybody I was trying to verify the following fact but I've been having some trouble.
I need to prove that if $A,B$ are two compatible observables and their eigenvalues are non-degenerate, then ...
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About the traditional explanation of the continuity of the first derivative of a 1D wavefunction
I would like to receive some clarifications about the traditional explanation of the continuity of the first derivative of a 1D wavefunction (E.g. see the very clear answer by @ZeroTheHero ...
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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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Doubt regarding measurement of spin in quantum mechanics as per 1st chapter of Quantum Mechanics, A Theoretical Minimum by Leonard Susskind
Susskind starts with an experiment in which he measures the spin of a particle , which can either take a value of $+1$ or $-1$ along any particular axis. He takes a measuring device $\mathcal A$ which ...
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What's the difference between observable and unobservable objects in a physical theory?
Both can help explain physical effects, but I'm looking for a rigorous definition of “observable” and “unobservable.”
For example, how is the experimental evidence for the existence of particles such ...
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Do position and spin commute?
I recently learned that position vectors and spin vectors lie in different spaces, and the complete wave is the tensor product of both. I wanted to know that whether we can talk about commutation of ...
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Dependency of dimension of Hilbert space of wavefunction on the chosen observable
I am assuming that the wave functions contain all the possible information about the system, how is it then for some observables like spin, the wave function can be expressed as a linear combination ...
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Can we find momentum in finite square well potential?
Can we find momentum in finite
square well potential? If so how can we find it? Does the eigenfunction of momentum operator is same as eigenfunction of Hamiltonian operator?
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Showing that time ordering does not matter for the measurement of commuting observables
Suppose I have two observables $R$ and $S$ who are represented by operator $R$ and $S$ which commute (I will hereafter ignore the distinction between observables and the operators representing them), ...
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Relationship between anti-commutators and correlation
Ballentine (in his solution at the back of the book to his Problem 8.10) writes that
$$[Tr(\rho \{A,B\}/2)]^2$$
is related to the correlation between the observables represented by $A,B$, but gives no ...
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Why can't linear combinations of superselection eigenspaces exist?
In his Quantum Mechanics: A Modern Development, Ballentine writes (page 184, second edition) that "It is sometimes asserted that states that would be described by vectors [which are linear ...
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$SU(2)$ vs. $SO(3)$ transformation, spinor rotation and measurement
Is it possible to measure the effects of $SU(2)$ rotations acting on spinor wave functions $\psi$ in the fundamental representation? That means, is it possible to extract information that ...
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Is wave function measurable?
I apologize for the length of this naive question. I am not sure it is appropriate for this community.
Is wave function measurable?
This is really a question in Atomic and Molecular Optics.
I hear ...
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The use of unitary operators in translating between reference frames in quantum mechanics
In Chapter 2.6 of his Lectures on groups and vector spaces for physicists, Isham describes how different observers (different reference frames) must describe the same quantum system.
Consider two ...
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How do quantum numbers combine when two quantum systems combined?
Quantum numbers are sometimes additive (e.g., baryon number, lepton number, $3$-component of the angular momentum, etc), sometimes multiplicative (e.g., parity), and at times, neither additive nor ...
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Quantum mechanics basic postulates [closed]
let me change the question. consider a wave function.
$$\varphi(x)$$
It is considered as a good wave function if it satisfies the following conditions.
it is a function meaning it is defined for all ...
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Causality and uncertainty principle
Suppose one measures the position, then momentum, then position of a particle, and that all these measurements are done in quick succession of one another (ie. arbitrarily close to zero-time as ...
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Why aren't the Standard Model predictions of $R(D)$ and $R(D^\ast)$ equal to 1?
The observables $R_K$ and $R_{K^\ast}$ are defined as
$$R_{K,K^*}(q_a^2, q_b^2) = \frac{\int_{q_a^2}^{q_b^2} \frac{d \Gamma (B^{(+,0)} \rightarrow K^{(+, \ast 0)} \mu^+ \mu^- )}{dq^2} dq^2}{\int_{q_a^...
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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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Geometrical representation of Angular Momentum [closed]
In the book by Nouredine Zettili of quantum mechanics, he discusses about the geometrical representation of quantum mechanics. I have a conceptual doubt related to it?
How does he diagrammatically ...
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What does "support of an observable" mean in quantum mechanics? [duplicate]
I am reading Preskill's lecture notes on quantum information. At one place he has written that the observables who live in a Hilbert space $H_A$ have access only to observables with support in $H_A$. ...
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Understanding exception to: Two non-commuting Hermitian operators commute with the hamiltonian implies degenerate energy eigenvalues
For context, I am working through the exercises in Modern Quantum Mechanics by Sakurai and Napolitano Second Ed. I have previously completed (years ago in undergrad) the Griffiths 3rd ed. Introduction ...
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Is this the Format of the Observable Universe?
The way I have it is: the Observable Universe looks as follows. In some ball, all the galaxy clusters exist, then in a bigger concentric ball the dark ages exist (no galaxies), then on the surface of ...
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What happens to the wave function after it collapses?
If a quantum particle is described by a certain wave function and we express it as superposition of for example its possibles energy states, after we measure it the wave function collapses and we ...
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Observable of a Part of a Composite Systems in QM [closed]
Let $A$ and $B$ be two spin$\frac12$ particles. The state of the system composed by $A$ and $B$ is the tensor product of the state of the two particles. Each particle has a base for the relevant ...
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Are energy eigenfunctions of a particle in one dimensional box orthogonal to each other?
For a particle in one dimensional box, its State Ψ(t=0) is defined as:
$Ψ= \frac{3}{5}Φ_1(x)+\frac{4}{5}Φ_3(x)$
I want to find out $|Ψ(0)|^2$.
My question is that as energy eigenfunctions $Φ_1(x)$ and ...
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Angular momentum addition in QM [duplicate]
If we consider the addition of orbital sngular momentum L and spin angular momentum S to produce the total angular momentum vector J, then J is a member of the vector space that is constructed by ...
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Why is there no uncertainty principle for mass or charge? [closed]
The uncertainty principle holds for pairs of certain observables, such as position and momentum.
All these observables have a relation to spacetime.
Other particle properties, by contrast, such as ...
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If two models generate identical predictions, must one be mathematically reducible to the other?
If two models always generate identical predictions of measurable observables given identical inputs of measurements over a given domain, must one be mathematically reducible to the other over that ...
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Incompatible observables
Suppose that $A$ and $B$ are observables satisfying $[A, B] \neq 0$, and $|\phi\rangle$ is an eigenstate of $A$. Then is it necessarily the case that $|\phi\rangle$ can be expressed as a superposition ...
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What happens when a projection observable produces a zero vector?
I'm new to quantum mechanics, but not quite as new to linear algebra and operator theory, and trying to understand the nature of observations from a mathematical perspective.
Consider a two-...
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Formula from wikipedia relating Heisenberg with Schrödinger pictures [duplicate]
I have a pretty naive question about a formula from wikipedia relating operator $A_H $ in Heisenberg picture with it's equivalent $A_S $ in Schroedinger picture:
$$ \frac{d}{dt}A_\text{H}(t)=\frac{...
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Is a quantity calculated from observables, observable?
I am not a physicist, and not sure whether I want the adjective, or the noun, observable here.
Example 1) If we view the mass and velocity of a classical particle as observables, we
calculate the ...
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Do physical quantities that appear in dot product in quantum mechanics always commute?
I am a sophomore learning quantum mechanics, and I got a confusion in my study, I tried to search for answers online but failed to find a satisfying answer. Hence, I wanted to post my question here ...
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Algebras of observables in classical physics. Are C*-algebras useful?
When studying the algebraic formulation of Quantum Mechanics, C-algebras are a very useful tool for dealing with algebras of observables. I have been studying whether all classical systems in physics ...
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Observables and RG flow
I am confused about a standard thing regarding renormalization group eqn. The primary motivation of writing the RG eqns are observables do not depend on the UV cutoff $\Lambda$ (Wilsonian) or ...
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Commuting observables and an eigenstate [closed]
Consider the observables $A$ and $B$ with $[A, B]=0$. Suppose that the state of the system satisfies the equation $A|a_1\rangle=a_1 |a_1\rangle$. After a measurement of the observable $A$, in what ...
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Can entanglement allow to predict deterministically results of incompatible measurements?
In my notes regarding entanglement and CHSH inequality it says:
Further, this is the case even for incompatible observables: measurements on one system allow us to predict with certainty the outcomes ...
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