We consider the goals of the introductory course in classical mechanics taken by physics majors and argue both that these goals are not well met in actual courses and that the goals themselves should be rethought. We propose alternative goals and describe an introductory ‘‘modern mechanics’’ course that addresses these alternative goals. Included in the description are several genres of homewor...

The time divergence of classical nonlinear response functions reveals the fundamental difficulty of dynamic perturbation based on classical mechanics. The nature of the divergence is established for systems in regular motions using asymptotic decomposition of Fourier integrals. The asymptotic analysis shows that the divergence cannot be removed by phase-space averaging such as the Boltzmann dis...

We consider here the coexistence of firstand third-order integrals of motion in two dimensional classical and quantum mechanics. We find explicitly all potentials that admit such integrals, and all their integrals. Quantum superintegrable systems are found that have no classical analog, i.e. the potentials are proportional to h̄, so their classical limit is free motion.

This letter briefly gives an overview of the theory proposed in quant-ph/9906130 and quant-ph/9909025 on the basis of quantum mechanics. Although quantum mechanics in twentieth century has succeeded to predict the correct results of large numbers of experiments in the process to find new fundamental particles in the nature, it seems to have left some fundamental open problems, both structural a...

This paper proves that protomechanics, previously introduced in quant-ph/9909025, deduces both quantum mechanics and classical mechanics. It does not only solve the problem of the arbitrariness on the operator ordering for the quantization procedure, but also that of the analyticity at the exact classical-limit of h̄ = 0. In addition, proto-mechanics proves valid also for the description of a ha...