Null oscillations

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According to quantum mechanics, in agreement with the uncertainty principle, every oscillator (harmonic or unharmonic) can never be at rest, but must always oscillate and be at one of discrete energy levels. For a quantum harmonic oscillator the energy at the n-th level is given by:

                En = hν(n + ½) 

where h is the Planck constant, ν is the frequency of the oscillations and n=0,1,2,....., . So the lowest energy that a harmonic oscillator can have (so called zero-point energy) is E_o = ½hν. Then it is in its ground state and performs null oscillations, according to quantum mechanics.

References:

1) W. Haken, H.C. Wolf: The Physics of Atoms and Quanta. Introduction to Experiments and Theory. Springer Verlag, Berlin Heidelberg 1994.

2) J. Avery: Quantum Theory of Atoms, Molecules and Photons. McGraw-Hill, New York 1972.

3) C. Cohen-Tannoudji, B. Diu, F. Laloe: Quantum Mechanics I and II, 2nd edition. Wiley, New York 1977.

4) A. Messiah: Quantum Mechanics I and II. Halsted, New York 1962.