Fundamental Notions of Quantum Mechanics

  • B. L. van der Waerden
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 214)


According to Wave Mechanics, a pure state1 of a mechanical system is defined at any time by a wave function Ψ. The mechanical systems considered in this book are systems such as atoms or molecules, each consisting of a finite number of particles (electrons and nuclei). The wave function Ψ is a complex-valued function of the coordinates of the particles, dependent on time, which is supposed to satisfy Schrödinger’s equation
$$ H\Psi + \frac{h}{i}\frac{{\partial \Psi }}{{\partial t}} = 0 $$


Hilbert Space Quantum Mechanics Spherical Harmonic Energy Operator Symmetric Operator 
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  1. 2.
    H.Lebesgue: Leçons sur L’integration. Paris: 1904.Google Scholar
  2. 5.
    See.J.von Neumann’s fundamental paper: Allgemeine Eigenwerttheorie Hermetischer Funktionaloperatoren. Math.Ann.102.p.49 (1929).Google Scholar
  3. 6.
    T. Kato Fundamental Properties of Hamilton operatprs of Schroedinger Type. Transactons Amer.Math.Soc,70, 195(1951)Google Scholar
  4. 10.
    K.O.Friedrichs: Peturbation of Spectra in Hilbert Spaces. Math.Soc. (Providence 1965)Google Scholar

Copyright information

© Springer-Verlag Berlin · Heidelberg 1974

Authors and Affiliations

  • B. L. van der Waerden
    • 1
  1. 1.Mathematisches InstitutUniversität ZürichSwitzerland

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