Perturbation expansions for a class of singular potentials

Harrell's modified perturbation theory [Ann. Phys. 105, 379-406 (1977)] is applied and extended to obtain non-power perturbation expansions for a class of singular Hamiltonians H = -D^2 + x^2 + A/x^2 + lambda/x^alpha, (A\geq 0, alpha > 2), known as generalized spiked harmonic oscillators. The perturbation expansions developed here are valid for small values of the coupling lambda > 0, and they extend the results which Harrell obtained for the spiked harmonic oscillator A = 0. Formulas for the the excited-states are also developed.Comment: 23 page

Tests of the Standard Model Using Muon Polarization Asymmetries in Kaon Decays

We have examined the physics and the experimental feasibility of studying various kaon decay processes in which the polarization of a muon in the final state is measured. Valuable information on CP violation, the quark mixing (CKM) matrix, and new physics can be obtained from such measurements. We have considered muon polarization in K_L to mu+ mu- and K to pi mu+ mu- decays. Although the effects are small, or difficult to measure because of the small branching ratios involved, these studies could provide clean measurements of the CKM parameters. The experimental difficulty appears comparable to the observation of K to pi nu barnu. New sources of physics, involving non-standard CP violation, could produce effects observable in these measurements. Limits from new results on the neutron and electron electric dipole moment, and epsilon-prime over epsilon in neutral kaon decays, do not eliminate certain models that could contribute to the signal. A detailed examination of muon polarization out of the decay plane in KMU3 and radiative KMU2 decays also appears to be of interest. With current kaon beams and detector techniques, it is possible to measure the T-violating polarization for KMU3 with uncertainties approaching 0.0001. This level of sensitivity would provide an interesting probe of new physics.Comment: 24 pages, 3 figures, To be published in the International Journal of Modern Physics