# 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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### How is Zig-zag Motion Observable in Quantum Mechanics Given Wave Function Collapse?

I'm puzzled by a concept I read about in a physics text concerning quantum measurement. The text describes the potential to observe a "zig-zag" motion if one could capture images of an ...
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### What is the interpretation of the covariance of two quantum observables?

I have been studying the covariance matrix in continuous variable quantum systems and I am struggling to understand the interpretation of this object. In statistics the covariance measures the joint ...
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### If an electron is inside an atom, does the expected value of spin measurements also depend on the orbital wavefunction?

The total quantum state of an electron in an atom can be written as the product of the orbital wavefunction and a spinor representing its spin state, $\Psi = \psi(r,\theta,\phi) \otimes \chi$. Say you ...
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### Is Number Operator a Generalized Momentum?

In superconducting circuit, the number operator, $\hat{n}$, and phase operator, $\hat{\varphi}$ are conjugate pairs. Is $\hat{n}$ the canonical momentum, conjugate momentum, and also generalized ...
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### Wavefunction with determinate momentum

In page 100 Griffiths' Introduction to Quantum Mechanics, Griffiths states that the eigenvector of $\hat{p}$ in the position basis is $\frac{1}{\sqrt {2\pi\hbar}}e^{\frac{ipx}{\hbar}}$ and states that ...
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### Closed expression for expected values of $\hat{p}\,\,^{2j}$ for the vacuum state

I am wondering if there is a closed expression for the expected value $\left<0\lvert \hat{p}\,\,^{2j}\lvert 0\right>$ with $j\in\mathbb{N}$, where $\left|0\right>$ is the vacuum state of the ...
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### Equivalence of gauge-invariance and physical observable

This is somewhat philosophical than physics. In gauge theories, it is true (more like the first principle) that \text{ physical observable } \Rightarrow \text{gauge invariant} \end{...
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### Counterexample to the observable algebra of a region and its causal completion being the same

I was reading a paper by Ed Witten called "Algebras, Regions and Observers". It can be found here: https://arxiv.org/abs/2303.02837 A major theme is theorems relating the algebra of ...
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### Does compatibility of observables imply a measurement of the second observable is unnecessary?

If two operators $A$ and $B$ are compatible then their corresponding operators $\hat{A}$ and $\hat{B}$ share a common set of eigenfunctions. The eigenvalue-eigenfunction equation for each ...
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### Condition on unitary operator for real eigenstates of Hamiltonian

I'm working with the discrete-time quantum walk in which the evolution is described by the unitary operator - $$U = S(C\otimes I)$$ where $C$ is the coin operator (acts on spin degree of freedom of ...
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### Koopman-Von Neumann Classical Mechanics From $C^*$-Algebra Approach?

My main question is the following: Is it possible to derive Koopman-von Neumann (KvN) classical mechanics from the $C^*$-Algebra approach to physics (as described here) similar to how the usual ...
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### Doubts regarding Quantum Mechanics [closed]

I recently started with Quantum mechanics from The Principles of Quantum Mechanics by R. Shankar. I have studied Linear Algebra in my course already. I have also studied QM from D. J Griffiths(up to ...
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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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### "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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