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Quantum Mechanics

  • Heinrich Saller
Chapter
Part of the Fundamental Theories of Physics book series (FTPH, volume 163)

Abstract

It is not really a good strategy to follow the historical development of classical theory to quantum theory by “quantizing” a classical theory. Quantum theory is not only the change of a government; it is even the change of the constitution.

For example, a classical Lagrangian with the separation in a free kinetic and an interaction term is not a good starting point to solve a quantal bound-state problem. The ontology and interpretation of a quantum description are completely different from those of a classical one. A classical–quantum relationship and distinction may be found in the different representation structures of time and position operations. In classical mechanics, the time orbits are valued in position, \( t \mapsto \vec x\left( t \right) \), mass points have a position, and the concept of a “point particle” makes sense. In quantum mechanics, the time orbits are valued in a Hilbert space with probability amplitudes. Now, in quantum mechanics, there are also orbits of position (“of,” not “in”): The Schrödinger wave functions (“information catalogues”) for bound-state vectors are matrix elements of infinite-dimensional Hilbert representations of noncompact position operations \( t \mapsto \psi \left( \vec x \right) \). The concept of a mass point is very restricted. For example, it does not make sense to call an electron, e.g., “in” a hydrogen atom, a point particle, as there are no orbits in position.

Keywords

Principal Quantum Number Time Translation Position Representation Quantum Algebra Time Orbit 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.MPI für Physik Werner-Heisenberg-InstitutMünchenGermany

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