Hannover 2003 – wissenschaftliches Programm

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A: Atomphysik

A 17: Postersitzung 2

A 17.1: Poster

Donnerstag, 27. März 2003, 16:00–18:30, Poster

The Classical Face of Quantum Mechanics — •Michael Brieger — DLR, Institut für Technische Physik, Pfaffenwaldring 38-40, D-70569 Stuttgart

The harmonic oscillator is a paradigm for the seemingly unbridgeable gap between classical and quantum mechanics: It is classically unimaginable how, e.g., a linear harmonic oscillator should be able to exist only in stationary states with equally spaced energy eigenvalues. Classically, the only known stationary state is the situation when the particle is sitting at the bottom of the potential without kinetic energy. This is quantum-mechanically not possible because of the zero-point energy. Only the correspondence principle promises an asymptotic narrowing of the gap for high quantum numbers. The reason for this dilemma is the axiomatic claim that only the properties of eigenstates are physically observable. By using the quantum-mechanical calculus, it is quite easy to show that the contrary is true, namely, that the expectation values in nonstationary states consistently show all features of the familiar classical behavior. This is demonstrated for the linear and the isotropic two-dimensional harmonic oscillator. In the latter case, the stationary states with angular momentum are easily recognized as situations of dynamical balance.