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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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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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 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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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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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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A Projection Operator generated by the Eigenspaces of an Observable?

What does it mean for a projection operator on to a subspace of Hilbert space for a system $S$, $H_{S}$, to be generated by the eigenspaces of an observable $A$ that correspond to a certain set $\...
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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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What is the meaning of rotating the frame in quantum mechanics?

I want to ask about the meaning of rotating the frame in quantum mechanics. Many papers write the rotating frame and I'm not sure what the meaning of it.
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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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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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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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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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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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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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Why does gravity forbid local observables?

I heard in a conference that gravity forbids to construct local gauge invariants like $\mathrm{Tr}\left\{−\frac{1}{4} F_{μν}^{a}F_{a}^{μν}\right\}$ and only allows non-local gauge invariant quantities ...
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Is mass an observable in Quantum Mechanics?

One of the postulates of QM mechanics is that any observable is described mathematically by a hermitian linear operator. I suppose that an observable means a quantity that can be measured. The mass ...
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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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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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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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Significance of exchange operator commuting with Hamiltonian

In an Introduction to Quantum Mechanics by Griffiths (pg. 180), he claims that "P and H are compatible observables, and hence we can find a complete set of functions that are simultaneous eigenstates ...
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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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