Sudden changes in the spectrum of a quantum system

An ion with internal degrees of freedom can be excited or deexcited when it is accelerated by an electric field and then suddenly reflected by a plane surface. When tthe internal motion is described by a single oscillator, the system is simple enough to allow the calculation of a large number of energy levels. The statistical properties of the spectrum and their dependence on the field strength and the mass ratio of the oscillator and the ion can then be investigated.