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With the help of molecular-dynamics computer simulations, we study the equilibrium con6gurations of systems of N =2 -5000 strongly correlated charged particles under the influence of a radial harmonic external confining force and their mutual Coulomb forces. The temperature is well below the crystallization point; i.e. , the ratio of Coulomb to kinetic energy is as large as 1 = 10 . The particles arrange in concentric spherical shells with approximately constant intershell distances. On the surfaces plane hexagonal structures are well pronounced. The calculated radii, occupation numbers, and energies per particle are compared with results of classical geometrical and shell models with homogeneously charged shells corrected for hexagonal surface occupation. The closed-shell particle numbers also agree well with those of multilayer icosahedra. From the computer simulations we extract a Madelung (excess) energy of -0.8926, which is close to the theoretical value of the shell model corrected for plane hexagonal surfaces, -0.8923, but larger than the one of the infinite geometrical lattice, -0.8944, and of the bcc value of -0.8959. Surface-energy eÃects are positive and of the order of N PACS number(s): 32.80. Pj, 52.25.b, 52.65.+z, 52.75.Di

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Two types of Hamiltonians are investigated which describe quantum mechanically a particle moving subject to a linear viscous force under the influence of a conservative force: the conventional explicitly time-dependent one and an alternative class of nonlinear Hamiltonians. In the latter group we propose a new form. By Ehrenfest’s theorem the expectation values of the operators of physical observables correspond to the classical quantities. For all Schrödinger equations we derive and discuss wavepacket, wave, stationary, and pseudostationary solutions of force free motion, free fall, and harmonic oscillator.