The quantum-mechanics tag has no usage guidance.

**3**

votes

**0**answers

220 views

### is there any connection between the consistent histories interpretation of quantum mechanics and kripke semantics?

Kripke semantics interpret intuitionistic logic by a partially ordered set of worlds/situations. Consistent histories interpretation of QM elaborates the copenhagen interpretation where a consistent ...

**-1**

votes

**2**answers

599 views

### Problem of quantization: state of the art

The "problem of quantization":
Find a vector space $Obs$ (as large as possible) of real-valued functions $f(p, q)$ on $R^{2n}$, containing the coordinate ...

**2**

votes

**2**answers

704 views

### Can one derive Wigner’s theorem in the complex case from the real case?

Wigner's theorem states that every symmetry of complex Hilbert space is either unitary or anti-unitary, up to multiplication by a unit scalar function. Here $f:\mathcal{H} \rightarrow \mathcal{H}$ is ...

**2**

votes

**1**answer

283 views

### Tracking down locality assumption in CHSH inequality

CHSH inequality requires both locality and realism. I will equate here realism with counterfactual definiteness.
Now counterfactual definiteness tells us that given two different measurements on the ...

**6**

votes

**2**answers

756 views

### Quantum mechanics basics [closed]

Hello. I'm thinking about where does the basic quantum mechanics things comes from. I mean the forms of operators and a Shroedinger equation. The more intuitive explanation is better.
To get forms of ...

**3**

votes

**1**answer

162 views

### Analytic continuation of instantaneous eigenstates of a time-dependent hamiltonian

We are considering the instantaneous eigenstates of an analytically time-dependent hamiltonian and I would like to know how legitimate it is to extend them to the complex plane.
Specifically, our ...

**8**

votes

**2**answers

2k views

### Classical Limit of Feynman Path Integral

I understand that in the limit that $\hbar$ goes to zero, the Feynman path integral is dominated by the classical path, and then using the stationary phase approximation we can derive an approximation ...

**12**

votes

**2**answers

3k views

### Classical Limit of Quantum Mechanics

There is a well-known principle that one can recover classical mechanics from quantum mechanics in the limit as $\hbar$ goes to zero. I am looking for the strongest statement one can make concerning ...

**6**

votes

**0**answers

229 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 graph-...

**2**

votes

**3**answers

414 views

### Cardinality of a certain set of distinct subsets of $\mathbb{N}$

A recent question here has convinced me that folks here have a warm heart for the foundations of quantum mechanics, so I decided to ask a question that has been bothering me for a while.
Quantum ...

**30**

votes

**1**answer

6k views

### “psi-epistemic theories” in 3 or more dimensions

In their recent paper The Quantum State Can Be Interpreted Statistically, Lewis et al. end with a very nice mathematical question, one whose answer (either way) would have interesting implications for ...

**12**

votes

**2**answers

694 views

### Is zero a hydrogen eigenvalue?

This question has been bugging me for some time.
Take the hamiltonian for the hydrogen atom: $$\hat{H}=-\frac{1}{2}\nabla^2-\frac{1}{r},$$ acting on (a domain contained in) $L^2(\mathbb{R}^3)$. It is ...

**2**

votes

**1**answer

1k views

### Square root of a stochastic process

I am currently working on the understanding of the stochastic nature of the Schroedinger equation. This has a notable history dating back to Nelson's works and relative criticisms. But one can take a ...

**2**

votes

**0**answers

330 views

### Quantum sheaves

Are the following definitions known?
Consider H a Hilbert space. A "quantum topology" on H is a set Sigma of closed subspaces satisfying the following conditions:
(a) {0} and H lie in Sigma
(b) If {...

**21**

votes

**3**answers

2k views

### On the periods in the periodic table (or Why is a noble gas stable?)

Added 22, November:
I've succeeded in making the question entirely unintelligible with all my additions.
So I thought I would summarize it in the simplest form I could manage and add it to the title. ...

**2**

votes

**1**answer

738 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 $\{\lambda_i^0\}$ ...

**47**

votes

**6**answers

4k views

### Is the Mendeleev table explained in quantum mechanics?

Does anybody know if there exists a mathematical explanation of the Mendeleev table in quantum mechanics? In some textbooks (for example in "F.A.Berezin, M.A.Shubin. The Schrödinger Equation") the ...

**10**

votes

**4**answers

2k views

### Topology on the space of Schwartz Distributions

If we equip the Schwartz space $\mathcal{S}$ with its usual Fréchet space topology, then the space of continuous linear functionals $\mathcal{S}^\ast$ is known as the space of Schwartz distributions ...

**3**

votes

**1**answer

432 views

### Are all quantum cellular automata invertible & representable?

A little background: As far as I know there is no standard definition of a quantum cellular automaton in the literature. Different authors use different definitions. Here I propose my own definition (...

**2**

votes

**2**answers

585 views

### Continuous Measurement in Quantum Mechanics

Let $\mathcal{P}(S^{\infty})$ denote the set of probability measures on the unit sphere $S^{\infty} \subset \mathcal{H}$ in the Hilbert space of states of a quantum mechanical system. Measurement of ...

**5**

votes

**2**answers

1k 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 ...

**7**

votes

**1**answer

618 views

### Can the von Neumann entropy of a positive, positive semi-definite, and unit-trace density matrix with equal on-diagonal terms be bounded by equalizing all off-diagonal elements to their highest/lowest value?

Statement of problem
Consider the density matrix $M = (m_{i,j})$ in $d$-dimensions with all positive elements: $m_{i,j} > 0$. From physics, a density matrix is Hermitian, positive semi-definite, ...

**5**

votes

**1**answer

836 views

### First Quantization is a mystery… but de-quantizing perhaps not

There is an well-known infamous DICTUM:
-Second Quantization is a functor, First Quantization is a mystery-.
Indeed, second quantization is the "Fock functor", which builds the Fock space in a ...

**7**

votes

**3**answers

1k 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 $...

**3**

votes

**0**answers

217 views

### Bell polytopes with nontrivial symmetries

Take $N$ parties, each of which receives an input $s_i \in {1, \dots, m_i}$ and produces an output $r_i \in {1, \dots, r_i}$, possibly in a nondeterministic manner. We are interested in joint ...

**24**

votes

**10**answers

4k 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 ...

**5**

votes

**1**answer

260 views

### Approximate analytic solution of Schroedinger equation with arbitrary power potential

I'm solving the following Schroedinger equation in the domain $r>0$
$\psi''(r) + \left(E-\frac{a}{r^b}\right)\psi(r)=0 $,
where $0 < b < 2$ and $a, E$ are positive constants. Primarily I'm ...

**35**

votes

**3**answers

4k views

### Quantum mechanics formalism and C*-algebras

Many authors (e.g Landsman, Gleason) have stated that in quantum mechanics, the observables of a system can be taken to be the self-adjoint elements of an appropriate C*-algebra. However, many ...

**7**

votes

**0**answers

332 views

### Quantizations in quantum mechanics

Perhaps this is not an appropriate question for MO, but having just discovered this site I wanted to ask it.
Is there a rigorous definition as to what "a quantization" of a Hamiltonian dynamical ...

**8**

votes

**1**answer

184 views

### Operator compression preserving lowest energy eigenspace.

I have a large ($10^6$ by $10^6$) sparse ($0.4$% nonzero) hermitian matrix $H$ arising from the discretization of an elliptic PDE. I would like to approximate $H$ with a smaller matrix $H'$ in such a ...

**10**

votes

**1**answer

1k views

### Wick rotation and the Riemann zeta function

The goal of this question is to conceptualize in some way the fact that the Riemann zeta function $\zeta(s)$, and other zeta functions like it, have analytic continuations.
Background
I have by now ...

**5**

votes

**1**answer

497 views

### Quantum probability experiment?

I am looking for an example (or definition) of a quantum probability experiment (if there is such a thing). Ideally it should have these properties:
Be purely mathematical; no mention of physics or ...

**1**

vote

**2**answers

609 views

### Quantum Error Correction

One can correct the errors in a quantum channel iff the coherent information of the input state is not reduced by the channel. This is analogous to sending quantum entanglement through a channel. If ...

**5**

votes

**1**answer

424 views

### What categorical mathematical structure(s) best describe the space of “localized events” in “relational quantum mechanics”?

In a recent (and to me, very beautiful) paper, entitled "Relational EPR",
Smerlak and Rovelli present a way of thinking about EPR which relies upon Rovelli's ...

**7**

votes

**2**answers

439 views

### Does there exist a potential which realizes this strange quantum mechanical system?

I have done some courses on quantum mechanics and statistical mechanics in the past. Since I also do math, I wonder about converge issues which are usually not such a problem in physics. One of those ...

**1**

vote

**0**answers

2k views

### Quantum computation implications of (P vs NP) [duplicate]

Possible Duplicate:
What impact would P!=NP have on the characterization of BQP?
Before I begin, I had a similar post closed for mentioning the recently released (to be verified) proof that P!=...

**11**

votes

**2**answers

2k views

### What impact would P!=NP have on the characterization of BQP?

Many complexity theorists assume that $P\ne NP.$ If this is proved, how would it impact quantum computing and quantum algorithms? Would the proof immediately disallow quantum algorithms from ever ...

**2**

votes

**3**answers

2k views

### Justification for the matching condition for the wave function at potential jumps. Why is it both restrictive enough and sufficiently general?

Consider Schrödinger's time-independent equation
$$
-\frac{\hbar^2}{2m}\nabla^2\psi+V\psi=E\psi.
$$
In typical examples, the potential $V(x)$ has discontinuities, called potential jumps.
Outside ...

**13**

votes

**1**answer

793 views

### Fixed point theorems and equiangular lines

I've been thinking about the equiangular lines (or SIC-POVM) conjecture, and my conclusion is that the best means of attack would be through some kind of fixed point theorem -- I'm thinking ...

**3**

votes

**2**answers

935 views

### Spectral decomposition for an arbitrary linear combination of position and momentum operators

Suppose we have the Hilbert space L2(Rn) and we have n operators Qi and n operators Pi defined in the usual way by:
Qi ψ(q1,q2,...,qn) = qi ψ(q1,q2,...,qn)
Pi ψ(q1,q2,...,qn) = -i $\frac{...

**2**

votes

**6**answers

2k views

### Functional Analysis and its relation to mechanics

Hi I'm currently learning Hamiltonian and Lagrangian Mechanics (which I think also encompasses the calculus of variations) and I've also grown interested in functional analysis. I'm wondering if there ...

**12**

votes

**1**answer

687 views

### Set theoretical realizations of the hidden variables program in quantum mechanics

The hidden variables program in quantum mechanics has been largely discredited by two powerful theorems, namely those of Bell and Kochen/Specker. Nonetheless, this program retains a certain ...

**3**

votes

**1**answer

498 views

### What is the entropy of a density matrix which is the sum of two unitarily equivalent projectors?

Construction
Suppose I have a density matrix $\rho$ which is proportional to a projector $P$ formed by tensoring together $N$ small projectors $P^{(i)}$ of rank 2:
$P^{(i)} = |a\rangle_i\langle a| + ...

**6**

votes

**3**answers

739 views

### Bounding a spectral gap: what proof techniques exist?

The following situation is ubiquitous in mathematical physics. Let
$\Lambda_N$
be a finite-size lattice with linear size
$N$. An typical example would be the subset of
$\mathbb{Z}\times\mathbb{Z}...

**3**

votes

**2**answers

456 views

### Simultaneous time-frequency concentration of orthonormal sequences?

Does there exist an orthonormal basis of square-integrable functions (either $L^2(\mathbb{R})$ or $L^2(\mathbb{C})$) such that the sequence of functions has bounded variance, and also the sequence ...

**27**

votes

**9**answers

5k views

### How is the physical meaning of an irreducible representation justified?

This is maybe not an entirely mathematical question, but consider it a pedagogical question about representation theory if you want to avoid physics-y questions on MO.
I've been reading Singer's ...

**11**

votes

**1**answer

717 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 "...

**0**

votes

**1**answer

247 views

### The Quantum Operations On The Bipartite Systems

Given two distinct and noninteracting quantum mechanical
systems $\mathfrak{S}\_1$ and $\mathfrak{S}\_2$ with state spaces
$\mathcal H\_1$ and $\mathcal H\_2$, respectively, the state space
of the ...

**26**

votes

**6**answers

3k views

### Why is addition of observables in quantum mechanics commutative?

I am no expert in the field. I hope the question is suitable for MO.
Background/Motivation
I once followed a quantum mechanics course aimed at mathematicians. Instead of the usual motivations coming ...

**1**

vote

**0**answers

629 views

### Tensor products as isomorphic functors in category theory

An earlier question that I posed sought to define a category with a set of quantum channels as arrows and the C$^{*}$-algebra that these channels map from and to as the object. So, for example, my ...