32,893 research outputs found
Lacunary Fourier series and a qualitative uncertainty principle for compact Lie groups
We define lacunary Fourier series on a compact connected semisimple Lie group
. If has lacunary Fourier series, and vanishes on a non empty
open set, then we prove that vanishes identically. This may be viewed as a
qualitative uncertainty principle
Coherent States for the Non-Linear Harmonic Oscillator
Wave packets for the Quantum Non-Linear Oscillator are considered in the
Generalized Coherent State framerwork. To first order in the non-linearity
parameter the Coherent State behaves very similarly to its classical
counterpart. The position expectation value oscillates in a simple harmonic
manner. The energy-momentum uncertainty relation is time independent as in a
harmonic oscillator. Various features, (such as the Squeezed State nature), of
the Coherent State have been discussed
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