# Tagged Questions

The quantum-mechanics tag has no wiki summary.

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### conjectures regarding a new Renyi information quantity

In a recent paper http://arxiv.org/abs/1403.6102, we defined a quantity that we called the "Renyi conditional mutual information" and investigated several of its properties. We have some open ...

**6**

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**0**answers

123 views

### From 3-framings on $\Sigma$ to $\mathrm{Spin}^c$-structures on $\mathrm{Loc}_G(\Sigma)$?

Here is my question, below that some motivation:
For $G$ a compact abelian Lie group and $\Sigma$ a surface, with $M_G = \mathrm{Loc}_G(\Sigma)$ denoting the space of flat $G$-connections on $\Sigma$ ...

**4**

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**0**answers

56 views

### $q$-deformations of fundamental equation of information and entropies

Classical information theory: fundamental equation of information
In classical information theory, the information $I(A)$ of an event $A$ (any element of the $\sigma$-algebra $\mathcal F$ of a ...

**10**

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**4**answers

757 views

### Can the equation of motion with friction be written as Euler-Lagrange equation, and does it have a quantum version?

My (non-expert) impression is that many physically important equations of motion can be obtained as Euler-Lagrange equations. For example in quantum fields theories and in quantum mechanics quantum ...

**2**

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**1**answer

342 views

### a question about geometric quantization background

I don't understand why for geometric description of a regular system, we take always the classical phase space as a symplectic manifold?

**3**

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**2**answers

59 views

### Proof the solution of von Neumann equation will fluctuate forever if Hamiltonian and initial density matrix does not commute

Given von Neumann equation
$$\frac{d}{dt} \rho(t) = -i [H, \rho(t)] = -i e^{-iHt}[H, \rho(0)]e^{iHt}.$$
If we know that $[H, \rho(0)] \neq 0$, how do we prove that the solution will fluctuate ...

**6**

votes

**3**answers

580 views

### Some explanation about Dynin's formalism

I have seen this claim on the Wikipedia page for the Yang-Mills Millenium problem by Alexander Dynin. He is a mathematician working at the Department of Mathematics of Ohio State University and so, I ...

**1**

vote

**1**answer

122 views

### Perturbation theory of eigenvalues - Effects of degeneracy/ multiplicity

In Quantum mechanics Schrödinger's perturbation theory is very important (see Wikipedia) which deals with perturbation of the discrete spectrum of a self-adjoint operator.
Where can I find a ...

**3**

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**0**answers

144 views

### Why is geometric quantization (esp. Berezin-Toeplitz quantization) interesting for a symplectic geometer/topologist?

I know that many symplectic geometers are interested in quantization as well.
From what I understood, quantization isn't expected to be used as a tool to answer symplectic questions (as in ...

**1**

vote

**3**answers

192 views

### How to evaluate the wiener measure of sets?

I would like to understand how the Wiener measure of some simple sets can be evaluated.
I will sketch the construction of Wiener measure I have in mind:
We denote the one point compactification of ...

**5**

votes

**3**answers

100 views

### graded generalization of the Moyal–Weyl product

Has anyone written about the graded generalization of the Moyal–Weyl product/star product, that is, where the original algebra is already graded? Is it just a matter of signs?

**8**

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**2**answers

578 views

### Mathematical equivalent to ladder operators?

A powerful method in theoretical physics are ladder operators. They are used in QM to solve problems like the harmonic oscillator and the hydrogen atom. The idea is to solve with their help the ...

**5**

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**3**answers

863 views

### Is there a useful generalization of the Schmidt decomposition to the tensoring together of 3 or more vector spaces?

I've rewritten the question in math notation, and I've left the old version in physics bra-ket notation here.
Background
A simple consequence of the singular value decomposition is that any vector ...

**1**

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**0**answers

109 views

### The Moyal action of a planar vector field

Let $X=P\frac{\partial}{\partial x}+Q\frac{\partial}{\partial y}$ be a polynomial vector field on $\mathbb{R}^{2}$. Consider the following (Moyal) derivation on $\mathbb{C}[x,y]$:
...

**4**

votes

**1**answer

107 views

### Closed form for 3j-symbol ratios

I am working on the spherical harmonic decomposition of cosmic microwave background maps, therefore I often deal with functions that are proportional to Wigner 3J symbols/Clebsch–Gordan ...

**4**

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**2**answers

150 views

### Integrals of two Bessel functions of the first kind and a modified bessel function of the second kind

I'm searching for a suitable (hopefully simple enough) solution to the following form of integral:
$$\int_0^\infty \mathrm{d}x~x^n J_\nu(a x) J_\nu(b x) K_\mu(c x) $$
Where $n$, $\nu$, and $\mu$ are ...

**2**

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**2**answers

170 views

### Lie group about the quantum harmonic oscillator [closed]

We konw that in quantum harmonic oscillator $H=a^\dagger a$, $a^\dagger$, $a$, $1$ will span a Lie algebra, where $a, a^\dagger$ is annihilation and creation operator, $H$ is the Hamiltonian operator. ...

**0**

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**0**answers

85 views

### Quantum Bayesian update and Bayesian update of a model category

We know that we can have internal categories in a model category. We also know that there is a notion of Quantum Bayesian update in a monoidal category. Does the Quantum Bayesian update (equation ...

**5**

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**2**answers

997 views

### Space with 720° / not 2$\pi$ rotational symmetry?

Is there a space with a 720°, but no 360° rotational symmetry? Possibly one that can be mapped onto something more conventional like R(3) or R(3,1)?
The reason I am asking is because in quantum ...

**9**

votes

**1**answer

539 views

### Which functions are Wiener-integrable?

I'm looking for either a few precise mathematical statements about Wiener integrals, or a reference where I can find them.
Background
The Wiener integral is an analytic tool to define certain ...

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145 views

### A “coarse” version of position operator and its properties

I am wondering if someone has ever studied the following operator in the context of quantum mechanics:
$$Q : L^2(\mathbb{R}) \to L^2(\mathbb{R})$$
$$(Q f)(x) := s(x) f(x),$$
where $s(x)$ is the ...

**1**

vote

**1**answer

268 views

### A question about complex polarization

Let $M$ be a symplectic manifold, Then a subbundle $P\subset TM^{\mathbf{C}}$ of the complexified tangent bundle is called a complex polarization if
$P$ is Lagrangian
P involutive
dim$P\cap\bar P ...

**1**

vote

**1**answer

154 views

### The set of leaves of the distribution $D$ on coadjoint orbit $O_{\mu}$

Let $G$ be a compact connected Lie group and $O_{\mu}$ be a coadjoint orbit where $\mu\in \mathfrak{g}^*$ and $\mathfrak{g}^*$ is the dual of the Lie algebra of $\mathfrak{g}=\mathrm{Lie}(G)$. Let ...

**4**

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**2**answers

207 views

### A Theorem by Von Neumann, which pertains a product of two Hilbert Spaces

I'm writing my thesis on the EPR paradox (I want to continue my master degree in physics) but I'm having an unusual problem. One passage from the book I'm following at the moment justifies one ...

**2**

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**1**answer

88 views

### Reference to complete derivation of Kossakowski–Lindblad equation and its steady solutions

Are there recommended textbook or good intro-reference to explain with complete stretch of Kossakowski–Lindblad equation especially how is the idea to derive it from ground?
...

**6**

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**0**answers

207 views

### Lovász function of the Möbius ladder

Quantum motivation
Noncontextuality inequalities (and in particular Bell inequalities) can be mapped into graphs, in such a way that its relevant properties can be calculated via some simple ...

**10**

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**3**answers

417 views

### Resource for learning quantum mechanics from the viewpoint of representation theory

Quantum mechanics is deeply connected with representation theory. Therefore, I'm looking for a textbook or article which presents quantum mechanics in a representation theoretic manner. Could anyone ...

**7**

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**2**answers

316 views

### $\mathrm{Bessel}^3$ Integral

I'm trying to calculate the following integral:
$\int_0^\infty \mathrm{BesselJ}[l_0,k_0r] \cdot \mathrm{BesselJ}[l_1,k_1r] \cdot \mathrm{BesselJ}[l_0-l_1,kr] \cdot r\,dr$
($\mathrm{BesselJ}[n,x]$ is ...

**3**

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**1**answer

122 views

### Cardinality of the set of Boolean subalgbras of the lattice of projections on a Hilbert space.

A simple question I've managed to gey myself quite confused about.
Given a Hilbert space H, what do we know about the cardinality of
(a) the set P(H) of projection operators onto H (equivalently, ...

**0**

votes

**1**answer

187 views

### Tensor product of generator of SU(n)

I'm doing research in quantum mechanics and got some trouble. Any help would be very much appreciated.
Let $\{\lambda_j\}$ be the set of generator of $SU(n)$. Consider the operator:
$K=\sum_j ...

**9**

votes

**1**answer

355 views

### Do quantum “Sure-Shor separators” have a natural Veronese/Segre classification? (question inspired by Gil Kalai and Aram Harrow)

Aram Harrow asked: "Is there any place this is written up?"
Update Partly in answer to Aram's question, the thermodynamical properties of varietal dynamical systems now are written-up in ...

**3**

votes

**1**answer

78 views

### Set of orthogonal simplexes or partial mutually unbiased bases

I am interested in the existence of a set of vectors $\{ v_{ij} \}_{ij} \subseteq \mathbb{C}^N$ for $i \in \{1,\dots,N\}$, $j \in \{1,\dots,N+1\}$ such that $\left\vert v^*_{ij} v_{ij'} \right\vert = ...

**2**

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**1**answer

82 views

### An example to show that when $P$ is a complex polarization the subbundle $P+ \bar P$ is not necessarly involutive

I start my question with some motivation. A subbundle $P\subset TM^{\mathbf{C}}$ of the complexified tangent bundle is called a complex polarization if
$P$ is Lagrangian
P involutive
dim$P\cap\bar ...

**25**

votes

**2**answers

831 views

### Is Langlands reciprocity somehow analogous to the wave-particle duality of quantum mechanics?

Apologies for the vague question, and for the many inaccuracies (I am not a physicist and barely a number theorist).
In physics, there is the notion of gauge group of a field theory. The gauge group ...

**2**

votes

**1**answer

133 views

### Eigenvalues of a matrix constructed with simple logic

If a matrix can be constructed with simple bit-logic operations, is it also possible to find Eigenvalues with logic?
First I'll just say that my knowledge of logic is pretty much limited to ...

**7**

votes

**1**answer

962 views

### What is the “Tangle” at the Heart of Quantum Simulation?

The following questions generalize and naturalize the question that was originally asked. Provisional answers largely due to Will Sawin are now included.
As was discussed in the question originally ...

**3**

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**0**answers

77 views

### Is there a known generalization of the Schmidt decomposition based on a maximal set of “locally orthogonal” vectors?

I came across the following unusual generalization of the Schmidt decomposition in my work, which I describe below. I would like to know if this structure has been studied before so I can read more ...

**2**

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**1**answer

589 views

### Bounding the von Neumann entropy of a density matrix with the Hilbert-Schmidt norm

Question
Suppose I have a $D$-dimensional density matrix $\rho_0$
$\rho_0^\dagger = \rho_0 \quad, \quad \mathrm{Tr} \rho_0 = 1 \quad, \quad \rho_0 > 0,$
with a known spectrum $\{\lambda_i^0\}$ ...

**6**

votes

**2**answers

337 views

### C*-algebraic representation of observables vs self-adjoint operators one

I am trying to reconcile the "physicist" definition of an observable: self-adjoint operator on a Hilbert space, and the operational one as given by Strocchi in "An introduction to the mathematical ...

**1**

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**0**answers

59 views

### Discretization model for Dirac equation in higher dimensions

I'm wondering if there are cases of discretization models (in lattices or graphs) that converge toward the non-linear Dirac equations? While there is a paper on the 2-d and 3-d cases ...

**17**

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**8**answers

1k views

### A novice question on Quantum Mechanics

I'm currently working through Dirac's book The Principles of Quantum Mechanics. In it, he describes the nature of superpositions and at one point states:
"... if the ket vector corresponding to a ...

**5**

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**4**answers

334 views

### Prequantization and Hilbert space

In the definition of pre-quantization on a symplectic manifold $(M,\omega)$, we represent a function $f\in C^{\infty}(M)$(with Lie algebra structure) to $\hat{f}$ in the Hilbert space $L^2(M,L,\mu)$ ...

**10**

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463 views

### Is quantum game theory reducible to classical game theory?

Quantum game theory is an extension of classical game theory to the quantum domain. It differs from classical game theory in three primary ways:
Superposed initial states,
Quantum ...

**5**

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**2**answers

216 views

### Certain partial integrations in quantum mechanics

In classical quantum mechanics (and specifically in the introductury texts on this topic) while calculating expectation values of certain operators in the Schrödinger approach we often have to do ...

**10**

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**2**answers

797 views

### Is there an equivalent of Heisenberg's uncertainty principle in the decision sciences ?

From memories of a quantum mechanics class and Wikipedia:
In quantum mechanics, the uncertainty principle is any of a variety of mathematical inequalities asserting a fundamental limit to the ...

**0**

votes

**1**answer

125 views

### Find a generalized hypergeometric-based function yielding certain ratios of fifth-degree polynomials

Find a (presumably, generalized hypergeometric-based function $f(n,a,k)$), yielding for $n=1, a=\frac{1}{2}$,the rational function (ratio of fifth-degree polynomials)
\begin{equation}
...

**2**

votes

**2**answers

215 views

### Existence of a projection operator onto a classical set of density matrices

I have a Hilbert space of quantum density matrices written in the Glauber-Sudarshan P representation - ie. we have coherent states $|\alpha \rangle$ and we write density matrices as
$$ \rho = \int ...

**1**

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277 views

### How to estimate the quantum fidelity between two given states

There is a well-known theorem, firstly obtained by Denes Petz, in quantum information theory, which is described as follows:
$\mathbf{Theorem.}$ Let $\rho$ and $\sigma$ be two states on $\mathcal H$, ...

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**1**answer

284 views

### Reconciling two notions of geometric quantization.

Let $(M,\omega)$ be a compact symplectic manifold and $(L,\nabla)$ a prequantum line bundle. There are two schemes to quantize this data:
Choose a polarization $P$ of $M$ and define the quantum ...

**24**

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**10**answers

3k views

### Toy Models of Quantum Mechanics

Do toy models of quantum mechanics help us better understand "regular" quantum mechanics? For example, if we look at quantum mechanics over a finite field $F$ (e.g. $\mathbb{Z}_2$), can this lead to ...