Springer eBooks

Linear Operators in Hilbert Spaces

Bernd Thaller

Published Jan 1, 2000• 2 citations

Publisher

DOI: 10.1007/0-387-22770-9_6

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We explore the basic mathematical physics of quantum mechanics. Our primary focus will be on Hilbert space theory and applications as well as the theory of linear operators on Hilbert space. We show how Hermitian operators are used to represent quantum observables and investigate the spectrum of various linear operators. We discuss deviation and uncertainty and briefly suggest how symmetry and representations are involved in quantum theory.

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Springer eBooks

Linear Operators in Hilbert Spaces

Bernd Thaller

Published Jan 1, 2000• 2 citations

Publisher

DOI: 10.1007/0-387-22770-9_6

Related papers

Preliminary: Hilbert Space and Linear Operators

Songbo Xie

Springer thesesJan 1, 20250 citations

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Matthew Gagne

Jan 1, 20131 citation

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Charles R. Giardina

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UnitextJan 1, 20130 citations

The Central Limit Theorem for random exponents on a Hilbert space in the Weak Operator Topology

Sviatoslav V. Dzhenzher

We consider random linear continuous operators $Ω\to \mathcal{L}(\mathcal{H}, \mathcal{H})$ on a Hilbert space $\mathcal{H}$ . For example, such random operators may be random quantum channels. The Central Limit Theorem is known for the sums of i.i.d. random operators. Instead of the sum, there may be considered the composition of random exponents $e^{A_i/n}$ . We obtain the Central Limit Theorem in the Weak Operator Topology for centralized and normalized random exponents of i.i.d. linear continuous operators on a Hilbert space.We consider random linear continuous operators $Ω\to \mathcal{L}(\mathcal{H}, \mathcal{H})$ on a Hilbert space $\mathcal{H}$. For example, such random operators may be random quantum channels. The Central Limit Theorem is known for the sums of i.i.d. random operators. Instead of the sum, there may be considered the composition of random exponents $e^{A_i/n}$. We obtain the Central Limit Theorem in the Weak Operator Topology for centralized and normalized random exponents of i.i.d. linear continuous operators on a Hilbert space.

arXiv:2510.04077Oct 5, 20251 citation

We consider random linear continuous operators

Ω\to \mathcal{L}(\mathcal{H}, \mathcal{H})

on a Hilbert space

\mathcal{H}

. For example, such random operators may be random quantum channels. The Central Limit Theorem is known for the sums of i.i.d. random operators. Instead of the sum, there may be considered the composition of random exponents

e^{A_i/n}

. We obtain the Central Limit Theorem in the Weak Operator Topology for centralized and normalized random exponents of i.i.d. linear continuous operators on a Hilbert space.