Berry Phase and Parametric Harmonic Oscillator

Abstract

Our concern in this section is once more with the time-dependent harmonic oscillator with Lagrangian

$$\displaystyle{ L = \frac{1} {2}\dot{x}^{2} -\frac{1} {2}\omega ^{2}(t)x^{2}\;. }$$

To present a coherent picture of the whole problem, let us briefly review some of the results of Chap. 21. There we found the propagation function