Mathematische Grundlagen der Quantenmechanik

von Neumann, J. (1932). Mathematische Grundlagen der Quantenmechanik. Springer.

Type

Book

Intellectual base

Review or monograph

Year

1932

DOI

10.1007/978-3-642-96048-2

ISBN

9783642960499

DOI registrant

Springer Nature

Link

https://link.springer.com/book/10.1007/978-3-642-96048-2

Cited from

physics

Cited by

4 citations across 4 artifacts.

Each citation links to the sentence it supports in the citing article.

Primes

• Entropy (Thermodynamic Sense)
  • The quantum analog, von Neumann entropy S = −Tr(ρ log ρ), extends the classical form to density-matrix formalism

    This sourceIntroduces the von Neumann entropy S(ρ) = −Tr(ρ log ρ), generalizing the Gibbs entropy to the density-matrix formalism of quantum mechanics.

• Measurement and Disturbance
  • This is distinct from measurement noise; disturbance is systematic change introduced by measurement, not random error in the measurement apparatus, a separation rigorously developed in von Neumann's (1932) mathematical formulation of measurement as a coupled-system interaction.

    This sourceCanonical mathematical formalization of quantum measurement as a coupled-system interaction; rigorously distinguishes apparatus-induced systematic state change (disturbance) from random measurement error (noise).

• Observer Effect
  • Quantum nondemolition (QND) measurement, pioneered by Wineland and colleagues (1979–1992) and formalized by Caves (1980), demonstrates a sophisticated approach to the back-action symmetry.
• Superposition

  • This sourceRigorous Hilbert-space formulation showing collapse as projection; establishes mathematical foundations for basis transformations.

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