Download PDF by Professor S. H. Patil, Professor K. T. Tang (auth.): Asymptotic Methods in Quantum Mechanics: Application to

By Professor S. H. Patil, Professor K. T. Tang (auth.)

ISBN-10: 3642573177

ISBN-13: 9783642573170

ISBN-10: 3642631371

ISBN-13: 9783642631375

Asymptotic equipment in Quantum Mechanics is a close dialogue of the overall houses of the wave features of many particle platforms. specific emphasis is put on their asymptotic behaviour, because the outer area of the wave functionality is such a lot delicate to exterior interplay. The research of those neighborhood houses is helping in developing easy and compact wave features for sophisticated structures. It additionally is helping in constructing a vast figuring out of alternative facets of quantum mechanics. As functions, wave features with right asymptotic types are used to systematically generate a wide info base for susceptibilities, polarizabilities, interactomic potentials and nuclear densities of many atomic, molecular and nuclear systems.

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Extra info for Asymptotic Methods in Quantum Mechanics: Application to Atoms, Molecules and Nuclei

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3, along with the values from some other calculations. The polarizabilities are generally in good agreement with the results of other calculations. 0276 as the input separation energy for H- . 2125 and the predicted value of the dipolar polarizability of H- is 220 which may be compared with the value of 211- 215 from earlier calculations. 3. 33 from other calculations. For the ions, there do not appear to be any reliable calculations. Since our wave functions have the correct asymptotic behaviour, we expect that the predicted values are quite reliable.

2. They are in good agreement with the results of elaborate calculations. 9037. 5276 from the elaborate variational calculations. Our expectation values for C2:::::i rIn) are equally good. Since the wave functions incorporate the correct asymptotic behaviour, the results for higher values of n are particularly reliable. Apart from the accuracy of the predicted energies, one can judge the quality of the model wave function in terms of the virial theorem. For the exact wave functions the virial theorem requires that the ratio -2T IV should be 1, where T and V are the average values of the kinetic energy and potential energy respectively.

2 S. H. 3) 42 4. Polarizabilities and Dispersion Coefficients Thus the change in the energy of the system is given in terms of its dipole polarizability a1. More generally, for a spherically non-isotropic system, we have Pi = aijej in the usual tensorial notation with aij being the polarizability tensor and a corresponding energy of -(1/2)aijeiej. Here we will consider only the spherically isotropic case. 4) where the summation is over the electrons in the system and we are using atomic units. 5) where the primed summation excludes the n = 0 term.

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Asymptotic Methods in Quantum Mechanics: Application to Atoms, Molecules and Nuclei by Professor S. H. Patil, Professor K. T. Tang (auth.)

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