Quantum Theory in a Nutshell

  • Dirk Dubbers
  • Hans-Jürgen Stöckmann
Part of the Graduate Texts in Physics book series (GTP)


In principle, the two-state quantum system can be discussed in an elegant and short manner by employing various subtle operator techniques. We do not follow this route. Instead, we go one by one through all essential steps. We first establish the spin matrices for spin one half. It turns out that the most general 2×2 Hamiltonian matrix can be expressed in terms of the Pauli spin matrices. Therefore, every two-state quantum system, whatever the underlying interaction, can be treated as an \(s = \frac{1}{2}\) effective-spin system. We derive the expectation values of energy- and spin-operators and their uncertainties, and we solve the two-state Schrödinger equation for two simple cases.


Spin Operator Magnetic Dipole Moment Spin Vector Zeeman Effect Vector Operator 
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  1. Feynman, R.P., Vernon, F.L. Jr., Hellwarth, R.W.: Geometrical representation of the Schrödinger equation for solving maser problems. J. Appl. Phys. 28, 49–52 (1957) ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Dirk Dubbers
    • 1
  • Hans-Jürgen Stöckmann
    • 2
  1. 1.Fak. Physik und Astronomie, Physikalisches InstitutUniversität HeidelbergHeidelbergGermany
  2. 2.Fachbereich Physik Philipps-Universität MarburgMarburgGermany

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