The quantum-mechanics tag has no wiki summary.

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### 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**

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**3**answers

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### 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 ...

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votes

**1**answer

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### 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 ...

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### 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 ...

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### 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 ...

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**1**answer

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### 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 ...

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votes

**1**answer

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### 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| + ...

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641 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
...

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**2**answers

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### 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 ...

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### 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 ...

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**1**answer

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### 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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**1**answer

240 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 ...

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votes

**6**answers

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### 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

604 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 ...

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votes

**4**answers

632 views

### Quantum channels as categories: question 1.

A quantum channel is a mapping between Hilbert spaces, $\Phi : L(\mathcal{H}_{A}) \to L(\mathcal{H}_{B})$, where $L(\mathcal{H}_{i})$ is the family of operators on $\mathcal{H}_{i}$. In general, we ...

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**3**answers

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### Are the Gell-Mann matrices extremal when used as Kraus operators for a quantum channel?

Landau and Streater proved that a set of Kraus operators, Ai, is extremal if and only if the set
$\{A_{k}^{\dagger}A_{l}\}_{k,l \ldots N}$
are linearly independent. I have seen very convincing ...

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### Noether's Theorem in Quantum Mechanics

In classical mechanics:
If a Lagrangian L is preserved by an infinitesimal change in the state space variables qi -> qi + εKi(q) leads to only second order change in the Lagrangian:
$$ 0 = ...

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votes

**3**answers

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### What is the relationship between algebraic geometry and quantum mechanics?

The basic relationship in algebraic geometry is between a variety and its ring of functions. Arguably a similarly basic relationship in quantum mechanics is between a state space and its algebra of ...

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### Where does a math person go to learn quantum mechanics?

My undergraduate advisor said something very interesting to me the other day; it was something like "not knowing quantum mechanics is like never having heard a symphony." I've been meaning to learn ...