By Giuliano Preparata

Dr. Preparata (d. 2000), a professor at an unspecified Italian college, used to be one of the minority of theoretical physicists hard the traditional version of quantum box conception with a "more life like" quark version of the user-friendly debris of topic. He argues his case in 5 lecture-type essays. An appendix overviews the underlying math and formal common sense. Lacks an index"

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A ) . m. field with frequency tv = (E2 — Ei) in resonance with the atomic transition 1 o 2, and the fourth term represents the electromagnetic coupling of the two atomic levels. m. field. m. * Thus the analysis that follows focusses on the physics of a single CD. m. field amplitude, a = a(t)e~lult, the time-dependence of the envelope a(t) can be neglected. If one does not make this approximation which, as we shall see, clearly breaks down in the highly condensed matter limit, the one-mode Lagrangian that appears in the phase of the PI is§ i • 1 .

2) exhibits in a particularly transparent way the fundamental role that the Hamiltonian operator plays in determining the dynamical evolution of the quantum system. 5) by virtue of the Hermiticity of the Hamiltonian operator. 6) which, due to the unitarity of exp~* H t , remains normalized at all times t. The fundamental fact that the Hamiltonian is the generator of the unitary transformations of the Hilbert space of the physical states associated with the dynamical evolution of the quantum system, puts the complete set of the eigenvectors of H, the energy eigenvectors, in a special and privileged position.

71=0 V \"H" V / ^•fl^HQW^HV.. 3 The Path Integral (PI): classical trajectories and Quant u m Physics Thanks to Dirac [Dirac (1933)] and later Richard Feynman [Feynman (1948)] that we possess today a very powerful and illuminating tool — the Path Integral — to fully appreciate the conceptual steps involved in the transition from classical to quantum physics, with respect to both the kinematical and the dynamical aspects. The Path Integral (PI) proves also very effective in giving straightforward and intuitive solutions to a few quantum mechanical problems, where the operator formalism in a Hilbert space tends to obscure the physical meaning of the calculations.

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