Abstract
The opening Chaps. (1–3) embark upon a nonlinear (NL) reformulation of quantum mechanics in terms of complex Riccati or the equivalent real Ermakov equations. To provide a solid foundation for the development of such a NL formulation of quantum theory, time-dependent (TD) quantum mechanics of systems with analytic solutions , i.e., Hamiltonians at most quadratic in position and momentum are used as starting point. The harmonic oscillator , the parametric oscillator and (in the limit \(\omega \rightarrow 0\)) the free motion are specifically considered. The corresponding Gaussian wave packet (WP) solutions of the conventional Schrodinger equation (SE) are completely determined by two parameters: their maximum and width; in these cases, both may be TD. The time-dependence of the WP-maximum, that is actually identical to the mean value of position \(\langle x \rangle \), calculated with this WP is trivial.
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