Date of Award


Degree Type


Degree Name

Doctor of Philosophy


Part I. A new method of calculating local densities of states from the moments of the Hamiltonian is developed and studied. A finite number of moments of the Hamiltonian at a given lattice site are first calculated. The quadratic Pade approximant, which is a special case of the Hermite-Pade approximant, is then used to obtain an approxi- mation for the local Green function. The local density of states is then obtained from there.;The new method was tested on several cases, which included regular lattices, a regular binary alloy, the semi-infinite simple cubic lattice, and a realistic model for the valence band of silicon. The results have been compared with those obtained from other methods.;The new method produces fairly accurate results in most parts of the energy band(s) if the number of singularity points is small. The accuracy obtained is comparable to or better than that of other methods of similar generality and complexity.;Part II. A square potential well can be experimentally fabricated, and used in quantum well lasers. By irradiating it with a driving laser beam the quantum well laser can be made tunable.;When the number of quantum emergy levels is fairly large, the behaviour of the electrons in the well can be studied by means of classical dynamics. The presence of the oscillating laser field causes the motion of the electrons to become stochastic, and thus they can escape from the well into the conduction band.;Stochasticity and ionisation have been studied by looking at the solutions to the classical equations of motion. Their dependence on the frequency and intensity of the driving laser has been studied for square wells of different dimensions.;The classical ionisation rate has been found to bear the charac- teristics of a multiphoton ionisation process. This unusual behaviour has been explained as the effect of the higher harmonics of the oscillating square potential well, as seen by the electron.;Finally, an experimental study of this physical system has been suggested, in which the classical predictions of this study can be tested.



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