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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Why is that in quantum mechanics quite often the physical observable is represented by Hermitian operator? [duplicate]

My knowledge in vector space and quantum mechanics is weak and I am trying to understand and make sense of the question that I asked. It will be very helpful if someone could explain it to me in a ...
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Relationship between symmetries and quantum operators of classical quantities?

I noticed this the other day. I don't really know "what" this means, I'd love to understand. The energy operator is $\hat E = -i \hbar \frac{\partial}{\partial t}$. Conservation of energy ...
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In quantum mechanics how the expression of average value of an observable is derived?

In Dirac's Principles of QM following is stated: $$ \langle x | A + B | x \rangle = \langle x | A | x \rangle + \langle x | B |x \rangle $$ but $$ \langle x | AB | x \rangle \ne \langle x | A | x \...
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Why do we care about the spectrum of the Hamiltonian?

I am just starting to solve the first couple of didactic problems of quantum mechanics, particles subjected to really simple Hamiltonians. Before checking them out I was thinking that the best ...
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Confusion about quantum field in AQFT

As far as I known, quantum field is defined by operator-valued distribution mathematically. If I understand correctly, in AQFT, we use self-adjoint elements of $C$* algebra to describe algebra of ...
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What extra observable(s) are needed to label the basis states of a representation of the rotation group $N$-dimensional space?

In $3$-dimensional space, any given irreducible representation of the rotation group has a basis whose states are uniquely labeled by the eigenvalues $m$ of a single observable $J_z$, which is one of ...
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Ehrenfest theorem application to harmonic oscillator

What are the Ehrenfest theorems for the harmonic oscillator potential $V(\textbf r)=\frac{1}{2}m\omega^2\textbf r^2$? So I understand the proof behind the Ehrenfest theorems: $\frac {d⟨\textbf r⟩}{dt}=...
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Is the number density of photons frame dependent?

In a relativistic context, the energy of a "single" photon, thought of as a massless particle with an on-shell condition $p^2=0$ or $E^2=\vec{p}^2$, depends on the frame. In other words, ...
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When studying the hydrogen atom, why do we seek simultaneous eigenfunctions of $\hat{L}^2$, $\hat{L}_z$, and $\hat{H}$?

When solving the Schrödinger equation for the hydrogen atom, textbooks invariably work in a more constraint situation, whereby not only an eigenfunction for the Hamiltonian operator $\hat{H}$ is ...
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What are all the known physical conjugate pairs?

According to the uncertainty principle, certain pairs of physical quantities are complementary variables. Wikipedia has a list: Energy <> Time Linear Momentum <> Position Angular Momentum ...
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Does the notion of observable was 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 ...
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Variance of an observation of an arbitrary state measured consecutively by two operators

If A and B are two commuting observables, and the observable A is first measured on an arbitrary state, and then B is measured on the resultant state, what is the variance in the last observation?
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What are possible experimental (optical/microscopic/spectroscopic) observables for identifying and differentiating superconductivity?

In a system one is analysing for superconductivity signatures, what are possible experimental (optical/microscopic/spectroscopic) observables for identifying and differentiating superconductivity?
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Density matrix of coherent state

The eigenstate of the annihilation operator $a$ is given by the state $a\mid \alpha \rangle = \alpha \mid \alpha \rangle$. In the Fock state basis, we can expand this state as $$\mid \alpha \rangle = ...
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If neutronium existed out there, are we capable of observing it? [duplicate]

I know that theoretically, neutronium cannot exist. However, no work was done until now even looking for neutronim around us. So my question is that, if neutronium actually existed with some minimum ...
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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| {...
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What do the quantum fields represent, mathematically?

I am looking for insight on quantum field theory, and more precisely, I am interested in having a low-detailed idea of what a quantum field theory is about; moreover, I should say hat I am a ...
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A question regarding the commutators of operators

Suppose we have got a triple of observables $A,B$ and $C$. Suppose furthermore, that $[A,B]=0$ and $[B,C]=0$ but $[A,C]\neq 0$ . Suppose, also now we do a measurement of $A$ then accordingly we would ...
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How to derive Ehrenfest's theorem?

$$\frac{d\langle p\rangle}{dt}=-i\hbar \int_{-\infty}^{\infty}\frac{d\psi^*}{dt} \frac{d\psi}{dx}+\psi^*\frac{d}{dt}\Bigr(\frac{d\psi}{dx}\Bigr)$$ I didn't know the coding of partial derivative which ...
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Non-observance and the Schrödinger equation

I was thinking today about configurations where one measures that a certain observable is not in a certain state. I was getting confused about what this means for decoherence. If I observe a detector ...
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Units of observables in quantum mechanics

Observables in quantum mechanics are described by Hermitian operators $\hat A: V \to V$, where $V$ is the Hilbert space of states. Examples include the $x$-coordinate operator $\hat x$, the $x$-...
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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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Compatible Observables in QM vs OQS

In elementary QM courses we always consider that components of momentum vector form a complete set of commuting observables. I am confused whether this is an input to our theory or whether we somehow ...
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Are static variables observables in QM?

I found the difference between dynamical and static variables explained here: https://physics.stackexchange.com/a/154977/239775 My question is: Are only dynamical variables represented by observables ...
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Effect of commuting observables on the probability of measuring a certain value [closed]

Say you can measure $3$ observables $(A, B, C)$ and you do the measurements in two different ways. $\newcommand{\ket}[1]{|#1\rangle} \newcommand{\bra}[1]{\langle#1|} \newcommand{\braket}[2]{\langle#1|#...
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Really why does promoting numerical variables to operators neatly work?

Apparently nice duality between classical and quantum mechanics first noticed by Dirac. As a graduate student of mathematics I believe such a wonderful similarity in their mathematics have a deep root ...
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Does the Heisenberg's uncertainty equation holds when one of the observable have zero variance?

From this link Heisenberg uncertainty principle, It says: Clearly, when $\Delta p_x$ shrinks, $\Delta x$ has to grow larger and larger in order to satisfy the Heisenberg inequality. For example, a ...
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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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Wavelength as an observable in quantum mechanics?

Recently I was discussing a problem with one of my students in which she found that two states of the particle in a box were orthogonal and was then asked to give an example of an observable that ...
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Does QM talk about reality in itself or our observation of it? [closed]

I am not a physicist and I've recently started watching introductory lectures on QM on youtube (MIT, Stanford) and reading the Feynman lectures. I have a high-school level knowledge of Math so I'm not ...
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How do Margenau and Park reach this conclusion?

I’m reading Isham’s Lectures on Quantum Theory and towards the end of Section 5.2.1, the last paragraph of page 96 starts with, Margenau and Park concluded from such arguments that, in general (not ...
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Physical Significance of non-normalized state

What does the coefficient physically mean for an operator that isn't an observable. For an observable the coefficient is the eigenvalue and is the value that will be measured, but for operators that ...
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Degeneracy and Complete Sets of Commuting Observables

I want to understand how the degeneracy of an operator is related to the existence of a complete set of commuting operators that includes it. I know that if a set of operators commute, they possess a ...
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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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Measuring the position of identical particles and wavefunction collapse

I'm working through Shankar's Principles of Quantum Mechanics, and I think I have hit a confusion over identical particles. The book refers to 'measuring the position' of two bosons to be $x_1$ and $...
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Eigenfunctions of compatible observables that are not shared

I'm using D.J. Griffiths's Introduction to Quantum Mechanics (3rd. ed), reading about the angular momentum operators $\mathbf L=(L_x,L_y,L_z)$ and $L^2$ in chapter 4. The author discusses ...
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Is the complete Hilbert space of a system, sum of the spans of position, momentum, energy, angular momentum spaces, etc?

What I understand is the following. 1) There is an abstract ket ( vector) which contains all the information about the system and it lives in an abstract vector space, the Hilbert Space which might ...
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What Is the logic and the intuition of the Heisenberg Uncertainty Principle based on? Is it Quantum Superposition or on the electromagnetic spectrum? [duplicate]

With many sources on the internet it has sort of become diluted as to how and why the Heisenberg uncertainty principle still makes sense. One claims that it is due to quantum superposition and that a ...
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Is there any operator in quantum mechanics that measure an observable with non-zero uncertainty?

What does a measurement do? The answer is: If the detector is designed to measure some observable O, it will leave the measured object, at least for an instant, in a zero-uncertainty state. I want to ...
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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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What is a physical example of an observable with degenerate eigenvalues? [closed]

If eigenvalues of an observable have the physical meaning of a possible result after a measurement, what's the interpretation of degenerate eigenvalues, and what is an example of such an observable?
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Why is the degeneracy in the eigenvalue representation of eigenkets always lifted when using a maximal set of commuting observables?

I don't see how this implicit theorem Sakurai states in his book on QM on page 31 can be proven in general Assume that we have found a maximal set of commuting observables; that is, we cannot add ...
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Is it possible for a quantum system to evolve out of a determinate state of some observable before measurement is made?

On page 96 of his book, Griffiths explains that determinate states of some observable $Q$ are eigenfunctions of that operator. So if a particle starts out in that state it will continue to be in that ...
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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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Expected value of operator or expected value of observable?

A question about terminology. I have seen both $\langle p\rangle$ and $\langle\hat{p}\rangle$ to calculate the expected value of momentum (same thing with position, energy etc.). The first one would ...
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How can you subtract a value from an operator/matrix?

I'm currently following Quantum Computation and Quantum Information by Nielsen & Chuang. I'm struggling to understand the derivation of The Heisenberg Uncertainty Principle in Box 2.4 page 89. I ...
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How to operationally realize the following type of equations of motion?

It is well known that for a free particle, described by $H=\hat{p}^2/2m$, $\hat{p}_{x}(t)=$ constant (similarly for other components of momentum). Meanwhile, $\hat{x}(t)$ is not a constant, being ...
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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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Irreducible representation and observables

Can any one explain why all observables can be associated with irreducible representation? I do not understand what is the relation between these two.
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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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