Quantum and classical worlds

Ionization electron escapes with kinetic energy = K e  

H SAMPLE CALCULATION I One-Electron Atom Ionization Energies. To calculate the ionization energy in of the Be ion, we find the magnitude of the 

Bohr s original model of the atom relied on a completely classical version of matter (with point charges for the nucleus and electron) and a completely quantum version of the radiation (with energy quantized into photons). The assumptions he had to make suggested that the picture remained incomplete, but this problem of how to complete the picture motivated the subsequent work to bring together the worlds of classical and quantum physics. In this section we see de Broglie s own justification of Bohr s assumptions, and the ramifications of the wavelike nature of particles on our ability to measure their properties. 

De Broglie s hypothesis can be used to justify two of Bohr s major assumptions, advancing the atomic model toward the picture we hold of the atom today. Bohr s assumption (II), that the electron does not radiate, is supported 

The circumference of the orbit, 2 nr for a particular state n, must be equal to some integer number n of electron de Broglie wavelengths  

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Analysis of this state is interesting from the point of view of the quantum measurement problem, an issue that has been debated since the inception of quantum theory by Einstein, Bohr, and others, and continues today [31]. One practical approach toward resolving this controversy is the introduction of quantum decoherence, or the environmentally induced reduction of quantum superpoations into clasacal statistical mbrtures [32], Decoherence provides a way to quantify the elusive boundary between classical and quantum worlds, and almost always precludes the existence of macroscopic Schrodinger-cat states, except for extremely short times. On the othm hand, the creation of mesoscopic Schrddinger-cat states like that of q. (10) may allow controlled studies of quantum decoherence and the quantum-classical boundary. This problem is directly relevant to quantum computation, as we discuss below. 

We may say that the range of the Pauli principle is infinity. If somebody paints some electrons green and others red (we do this in the perturbational method), they are in no man s land, between the classical and quantum worlds. Since the wave function does not have the proper symmetry, the corresponding operator + Hg... 

Ciccotti G and Ferrario M 1998 Constrained and nonequilibrium molecular dynamics Classical and Quantum Dynamics In Condensed Phase Simulations ed B J Berne, G Ciccotti and D F Coker (Singapore World Scientific) pp 157-77... 

Berne B J, Ciccotti G and Coker D F (ed) 1998 Classical and Quantum Dynamics In Condensed Phase S/mu/af/ons (Singapore World Scientific)... 

Classical and Quantum Mechanics. At the beginning of the twentieth century, a revolution was brewing in the world of physics. For hundreds of years, the Newtonian laws of mechanics had satisfactorily provided explanations and supported experimental observations in the physical sciences. However, the experimentaUsts of the nineteenth century had begun delving into the world of matter at an atomic level. This led to unsatisfactory explanations of the observed patterns of behavior of electricity, light, and matter, and it was these inconsistencies which led Bohr, Compton, deBroghe, Einstein, Planck, and Schrn dinger to seek a new order, another level of theory, ie, quantum theory. 

Jonsson H, Mills G, Jacobsen K (1998) In Berne BJ, Ciccotti G, Coker DF (eds) Nudged Elastic Band Method , in Classical and quantum dynamics in condensed phase simulations, World Scientific, Singapore, pp 387 101... 

MSN. 149. I. Prigogine, Classical and quantum mechanics of unstable dynamical systems, in Proceedings, International Conference on Dynamical Systems and Chaos, Y. Aizawa, S. Saito, and K. Shiraiwa, eds.. World Scientific, Singapore, Vol. 2, 1995. 

MSN. 153.1. Prigogine and T. Petrosky, Poincare Resonances and the Extension of Classical and Quantum Mechanics, in Nonlinear, deformed and irreversible quantum systems, H. D. Doebner, V. K. Dobrev, and P. Nattermann, eds.. World Scientific, Singapore, pp. 3-21, 1995. 

Berne, B.J., Ciccotti, G., Coker, D.F. (eds), Classical and Quantum Dynamics in Condensed Phase Simulations, World Scientific, River Edge, NJ, 1998. 

G. A. Voth, in Classical and Quantum Dynamics in Condensed Phase Simulations, edited by B. J. Berne, G. Ciccotti, and D. E Coker (World Seientifie, Singapore, 1998), Chap. 27, p, 647. 

M. W. Evans and L. B. Crowell, Classical and Quantum Electrodynamics and the B Field, World Scientific, Singapore, 1999. 

G. Ciccotti, M. Ferrario, D. Laria, and R. Kapral, in Progress of Computational Physics of Matter Methods, Software and Applications, L. Reatto and F. Manghi, Eds., World Scientific, Singapore, 1995, pp. 150-190. Simulation of Classical and Quantum Activated Processes in the Condensed Phase. 

Bose-Einstein condensates are unusual in numerous ways. With careful study physicists will gain basic knowledge about the material and quantum worlds. The atoms in a condensate are indistinguishable. All atoms move at the same speed in the same space. One can ask How can two objects occupy the same place at the same time A condensate is a macroscopic quantum wave packet and a macroscopic example of Heisenberg s uncertainty principle. Condensates hold the promise of bringing new insights to the strange world between the microscopic quantum and the macroscopic classical domains. 

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