# Questions tagged [quantum-mechanics]

For questions about mathematical problems arising from quantum mechanics, a branch of physics describing the behaviour of nature at very small scales, at the level of atoms and subatomic particles.

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### Literature on representations of SU(2) on the direct product of irreps [closed]

I am in the situation where the action of SU(2) has lead my Hilbert space to be block diagonalised into a direct sum of irreps. For example I might have the tensor product of two qubits, i.e ...
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### On commutator of bounded operators

Let $\mathbb H$ be a Hilbert space and let $\mathcal B(\mathbb H)$ be the bounded operators on $\mathbb H$. Let $J,K\in \mathcal B(\mathbb H)$ such that $J=J^*, K=-K^*.$ Then the commutator $[J,K]$ ...
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### How to derive the formulas of the spin-weighted spheroidal eigenvalues (2.16a)-(2.16g) in arXiv:gr-qc/0511111?

I am reading the article "Eigenvalues and eigenfunctions of spin-weighted spheroidal harmonics in four and higher dimensions", which is on https://arxiv.org/abs/gr-qc/0511111. I want to ...
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### Frobenius norm bounds on exponentials of anti-Hermitian matrices

Suppose $X$ and $Y$ are two anti-Hermitian matrices satisifying $\|X\|, \|Y\| \leq \pi$, where $\|\cdot\|$ is the spectral norm. I'm trying to prove the following bounds on the Frobenius norm of the ...
1 vote
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### A transformation game for natural numbers?

Consider the completely additive function $\eta(n) := \sum_{p\mid n} v_p(n)p$ defined on natural numbers, with values in natural numbers. For literature, on this function, see the corresponding OEIS ...
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### Moyal products of exponentials

I have trouble verifying a claim made by Sharan in his paper: https://doi.org/10.1103/PhysRevD.20.414. What he essentially claims is that the sequence of Moyal $*$-products \underbrace{\exp(-itH/n)*\...
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### Can two eigenfunctions be almost linearly dependent in a region?

Consider the Schrödinger operator $H=-\Delta+|x|^a$ on $\mathbb{R}$, where $a>0$. Since the potential is growing at $\infty$, we have compact resolvent thus the eigenvalues are discrete and tend to ...
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I recently learned about estimates one can perform with operators on $L^2(\mathbb{R}^n)$ given as $f(x)g(-i\nabla)$, see Chapter 4 in Trace Ideals and their Applications by Professor Barry Simon (the ...
von-Neumann entropy I know von-Neumann entropy on density matrix $S=-{\rm Tr}(\rho \ln\rho)$ is similar to Shannon entropy $S=-\sum_i p_i\ln p_i$ in classical mechanics. And I want to get Bose-...