Factorization of quantum mechanical potentials has a long history extending back to the earliest days of the subject. In the present paper, the non-uniqueness of the factorization is exploited to derive new isospectral non-singular potentials. Many one-parameter families of potentials can be generated from known potentials using a factorization that involves superpotentials defined in terms of excited states of a potential. For these cases an operator representation is available. If ladder operators are known for the original potential, then a straightforward procedure exists for defining such operators for its isospectral partners. The generality of the method is illustrated with a number of examples which may have many possible applications in atomic and molecular physics.

Factorization of quantum mechanical Hamiltonians has been a useful technique for some time. This procedure has been given an elegant description by supersymmetric quantum mechanics, and the subject has become well-developed. We demonstrate that the existence of raising and lowering operators for the harmonic oscillator (and many other potentials) can be extended to their supersymmetric partners. The use of double supersymmetry (or a factorization chain) is used to obtain non-singular isospectral potentials, and the explicit expressions for the ladder operators, wave functions and probability densities are provided. This application avoids the technical complexities of the most general approaches, and requires relatively modest methods from supersymmetric quantum mechanics.PACS numbers: 03.65. Ge, 03.65.Fd, 03.65.Ca In supersymmetric quantum mechanics (SUSY QM) the form of the Schrödinger equation of a particle is determined by its Hamiltonian ( = 2m = 1):where V (x) is nonsingular on −∞ < x < ∞ and has at least one bound state. If its ground state wave function ψ 0 and energy E 0 are known, then it is always possible to factor the Hamiltonian H (0) − = H − E 0 into a product of two linear differential operators:where W 0 (x) is the superpotential related to the potential V

We report on the measurement of defect densities and minority carrier lifetimes in nanocrystalline Si samples contaminated with controlled amounts of oxygen. Two different measurement techniques, a capacitance-frequency (CF) and high temperature capacitancevoltage techniques were used. CF measurement is found to yield noisy defect profiles that could lead to inconclusive results. In this paper, we show an innovative technique to remove the noise and obtain clean data using wavelet transforms. This helps us discover that oxygen is creating both shallow and deep/midgap defect states in lieu with crystalline silicon. Minority carrier lifetime measured using reverse recovery techniques shows excellent inverse correlation between deep defects and minority carrier lifetimes through which hole capture cross section can be evaluated.

We consider a multi-dimensional scalar wave equation with memory corresponding to the viscoelastic material described by a generalized Zener model. We deduce that this relaxation system is an example of a non-strictly hyperbolic system satisfying Majda's block structure condition. Wellposedness of the associated Cauchy problem is established by showing that the symbol of the spatial derivatives is uniformly diagonalizable with real eigenvalues. A long-time stability result is obtained by plane-wave analysis when the memory term allows for dissipation of energy.

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