Is the Lowest Order Supersymmetric WKB Approximation Exact for All Shape Invariant Potentials ?

It has previously been proved that the lowest order supersymmetric WKB approximation reproduces the exact bound state spectrum of shape invariant potentials. We show that this is not true for a new, recently discovered class of shape invariant potentials and analyse the reasons underlying this breakdown of the usual proof.Comment: 8 page

Gravitational uncertainties from dimension-six operators on supersymmetric GUT predictions

We consider the gravity induced dimension six terms in addition to the dimension five terms in the SUSY GUT Lagrangian and find that the prediction for $\alpha_s$ may be washed out completely in supersymmetric grand unified theories unless the triplet higgs mass is smaller than $7\times 10^{16}$ GeV.Comment: 7 pages,latex.Title of original version changed,text added and a figure has been added.Figure is available on request.To appear as a brief Report in Phys.Rev.

On Exactness Of The Supersymmetric WKB Approximation Scheme

Exactness of the lowest order supersymmetric WKB (SWKB) quantization condition $\int^{x_2}_{x_1} \sqrt{E-\omega^2(x)} dx = n \hbar \pi$, for certain potentials, is examined, using complex integration technique. Comparison of the above scheme with a similar, but {\it exact} quantization condition, $\oint_c p(x,E) dx = 2\pi n \hbar$, originating from the quantum Hamilton-Jacobi formalism reveals that, the locations and the residues of the poles that contribute to these integrals match identically, for both of these cases. As these poles completely determine the eigenvalues in these two cases, the exactness of the SWKB for these potentials is accounted for. Three non-exact cases are also analysed; the origin of this non-exactness is shown to be due the presence of additional singularities in $\sqrt{E-\omega^2(x)}$, like branch cuts in the $x-$plane.Comment: 11 pages, latex, 1 figure available on reques

New Eaxactly Solvable Hamiltonians: Shape Invariance and Self-Similarity

We discuss in some detail the self-similar potentials of Shabat and Spiridonov which are reflectionless and have an infinite number of bound states. We demonstrate that these self-similar potentials are in fact shape invariant potentials within the formalism of supersymmetric quantum mechanics. In particular, using a scaling ansatz for the change of parameters, we obtain a large class of new, reflectionless, shape invariant potentials of which the Shabat-Spiridonov ones are a special case. These new potentials can be viewed as q-deformations of the single soliton solution corresponding to the Rosen-Morse potential. Explicit expressions for the energy eigenvalues, eigenfunctions and transmission coefficients for these potentials are obtained. We show that these potentials can also be obtained numerically. Included as an intriguing case is a shape invariant double well potential whose supersymmetric partner potential is only a single well. Our class of exactly solvable Hamiltonians is further enlarged by examining two new directions: (i) changes of parameters which are different from the previously studied cases of translation and scaling; (ii) extending the usual concept of shape invariance in one step to a multi-step situation. These extensions can be viewed as q-deformations of the harmonic oscillator or multi-soliton solutions corresponding to the Rosen-Morse potential.Comment: 26 pages, plain tex, request figures by e-mai

On an asymptotic estimate of the nn-loop correction in perturbative QCD

A recently proposed method of estimating the asymptotic behaviour of QCD perturbation theory coefficients is critically reviewed and shown to contain numerous invalid mathematical operations and unsubstantiated assumptions. We discuss in detail why this procedure, based solely on renormalization group (RG) considerations and analyticity constraints, cannot lead to such estimates. We stress the importance of correct renormalization scheme (RS) dependence of any meaningful asymptotic estimate and argue that the unambiguous summation of QCD perturbation expansions for physical quantities requires information from outside of perturbation theory itself.Comment: PRA-HEP-92/17, Latex, 20 pages of text plus 5 figures contained in 5 separate PS files. Four of them (corresponding to Figs.1,2,3,5) are appended at the end of this file, the (somewhat larger one) corresponding to Fig.4 can be obtained from any of the mentioned E-mail addresses upon request. E-mail connections: J. Chyla - [email protected]) or h1kchy@dhhdesy3 P. Kolar - [email protected]

Quasi-classical path integral approach to supersymmetric quantum mechanics

{}From Feynman's path integral, we derive quasi-classical quantization rules in supersymmetric quantum mechanics (SUSY-QM). First, we derive a SUSY counterpart of Gutzwiller's formula, from which we obtain the quantization rule of Comtet, Bandrauk and Campbell when SUSY is good. When SUSY is broken, we arrive at a new quantization formula, which is found as good as and even sometime better than the WKB formula in evaluating energy spectra for certain one-dimensional bound state problems. The wave functions in the stationary phase approximation are also derived for SUSY and broken SUSY cases. Insofar as a broken SUSY case is concerned, there are strong indications that the new quasi-classical approximation formula always overestimates the energy eigenvalues while WKB always underestimates.Comment: 13 pages + 5 figures, complete paper submitted as postscript file, to appear in Phys. Rev.

Recurrent Coding Sequence Variation Explains only A Small Fraction of the Genetic Architecture of Colorectal Cancer

Whilst common genetic variation in many non-coding genomic regulatory regions are known to impart risk of colorectal cancer (CRC), much of the heritability of CRC remains unexplained. To examine the role of recurrent coding sequence variation in CRC aetiology, we genotyped 12,638 CRCs cases and 29,045 controls from six European populations. Single-variant analysis identified a coding variant (rs3184504) in SH2B3 (12q24) associated with CRC risk (OR = 1.08, P = 3.9 × 10-7), and novel damaging coding variants in 3 genes previously tagged by GWAS efforts; rs16888728 (8q24) in UTP23 (OR = 1.15, P = 1.4 × 10-7); rs6580742 and rs12303082 (12q13) in FAM186A (OR = 1.11, P = 1.2 × 10-

The balloon experimental twin telescope for infrared interferometry (BETTII): An experiment for high angular resolution in the far-infrared

The Balloon Experimental Twin Telescope for Infrared Interferometry (BETTII) is a new balloon-borne far-infrared interferometer, being designed to provide spatially-resolved spectroscopy in the far infrared (30–90 μm). The combination of an 8-meter baseline with a double-Fourier Michelson interferometer allows the identification and separation of closely-spaced astronomical sources, while also providing a low-resolution spectrum for each source. In this wavelength range, BETTII will provide subarcsecond angular resolution, a capability unmatched by other far-infrared facilities. This paper provides an overview of the entire design of the BETTII experiment, with a short discussion of the predicted performance on flight