Position Dependent Mass Schroedinger Equation and Isospectral Potentials : Intertwining Operator approach

Here we have studied first and second-order intertwining approach to generate isospectral partner potentials of position-dependent (effective) mass Schroedinger equation. The second-order intertwiner is constructed directly by taking it as second order linear differential operator with position depndent coefficients and the system of equations arising from the intertwining relationship is solved for the coefficients by taking an ansatz. A complete scheme for obtaining general solution is obtained which is valid for any arbitrary potential and mass function. The proposed technique allows us to generate isospectral potentials with the following spectral modifications: (i) to add new bound state(s), (ii) to remove bound state(s) and (iii) to leave the spectrum unaffected. To explain our findings with the help of an illustration, we have used point canonical transformation (PCT) to obtain the general solution of the position dependent mass Schrodinger equation corresponding to a potential and mass function. It is shown that our results are consistent with the formulation of type A N-fold supersymmetry [14,18] for the particular case N = 1 and N = 2 respectively.Comment: Some references have been adde

Assessment of the State-of-the-Art of System-Wide Safety and Assurance Technologies

Since its initiation, the System-wide Safety Assurance Technologies (SSAT) Project has been focused on developing multidisciplinary tools and techniques that are verified and validated to ensure prevention of loss of property and life in NextGen and enable proactive risk management through predictive methods. To this end, four technical challenges have been listed to help realize the goals of SSAT, namely (i) assurance of flight critical systems, (ii) discovery of precursors to safety incidents, (iii) assuring safe human-systems integration, and (iv) prognostic algorithm design for safety assurance. The objective of this report is to provide an extensive survey of SSAT-related research accomplishments by researchers within and outside NASA to get an understanding of what the state-of-the-art is for technologies enabling each of the four technical challenges. We hope that this report will serve as a good resource for anyone interested in gaining an understanding of the SSAT technical challenges, and also be useful in the future for project planning and resource allocation for related research

Pseudo-Hermiticity and some consequences of a generalized quantum condition

We exploit the hidden symmetry structure of a recently proposed non-Hermitian Hamiltonian and of its Hermitian equivalent one. This sheds new light on the pseudo-Hermitian character of the former and allows access to a generalized quantum condition. Special cases lead to hyperbolic and Morse-like potentials in the framework of a coordinate-dependent mass model.Comment: 10 pages, no figur

A New Class of PT-symmetric Hamiltonians with Real Spectra

We investigate complex PT-symmetric potentials, associated with quasi-exactly solvable non-hermitian models involving polynomials and a class of rational functions. We also look for special solutions of intertwining relations of SUSY Quantum Mechanics providing a partnership between a real and a complex PT-symmetric potential of the kind mentioned above. We investigate conditions sufficient to ensure the reality of the full spectrum or, for the quasi-exactly solvable systems, the reality of the energy of the finite number of levels.Comment: 9 pages, Late

SWKB Quantization Rules for Bound States in Quantum Wells

In a recent paper by Gomes and Adhikari (J.Phys B30 5987(1997)) a matrix formulation of the Bohr-Sommerfield quantization rule has been applied to the study of bound states in one dimension quantum wells. Here we study these potentials in the frame work of supersymmetric WKB (SWKB) quantization approximation and find that SWKB quantization rule is superior to the modified Bohr-Sommerfield or WKB rules as it exactly reproduces the eigenenergies.Comment: 8 page

Pseudo-Hermitian versus Hermitian position-dependent-mass Hamiltonians in a perturbative framework

We formulate a systematic algorithm for constructing a whole class of Hermitian position-dependent-mass Hamiltonians which, to lowest order of perturbation theory, allow a description in terms of PT-symmetric Hamiltonians. The method is applied to the Hermitian analogue of the PT-symmetric cubic anharmonic oscillator. A new example is provided by a Hamiltonian (approximately) equivalent to a PT-symmetric extension of the one-parameter trigonometric Poschl-Teller potential.Comment: 13 pages, no figure, modified presentation, 6 additional references, published versio

New approach to (quasi)-exactly solvable Schrodinger equations with a position-dependent effective mass

By using the point canonical transformation approach in a manner distinct from previous ones, we generate some new exactly solvable or quasi-exactly solvable potentials for the one-dimensional Schr\"odinger equation with a position-dependent effective mass. In the latter case, SUSYQM techniques provide us with some additional new potentials.Comment: 11 pages, no figur

DNA linkage based diagnosis of Wilson disease in asymptomatic siblings

Wilson disease (WD) is an autosomal recessive disorder caused by defects in ATP7B gene located in chromosome 13q14, and manifested as hepatolenticular degeneration as a result of accumulation of copper. No information on the mutation in the ATP7B gene and haplotypes using linked markers is available for WD patients in India. Hence, the present study was undetaken to identify, by a PCR-based molecular diagnostic test, presymptomatic siblings of WD affected individuals in families with multiple offspring. Methods: Genomic DNA was prepared from the peripheral blood of the patients, siblings and his/her first degree relatives. The repeat-markers flanking WD locus were amplified by PCR using fluorescent labeled primers. Amplified DNA fragments were analyzed by polyacrylamide gel electrophoresis in ABI 377 DNA sequencing system. Genotypes of the samples were determined using Genescan software. Haplotypes were determined based on segregation of the alleles in the families under study. Results: Among 15 WD affected families with multiple children, 4 cases were identified where younger siblings shared same genotype as the patient at all three markers analyzed. Further, eight different haplotypes were detected in the four patients. Interpretation & conclusion: The siblings of the WD patients carrying the same genotype at the markers linked to WD locus were presymptomatically diagnosed individuals. Presence of eight different haplotypes in the four patients suggested mutational heterogeneity at the WD locus. The test helps clinicians for therapeutic intervention in suspect WD cases by copper chelating agents prior to manifestation of overt clinical symptoms. Key words ATP7B - genotype - haplotype - microsatellite - Wilson disease (WD) is a genetic disorder, which manifests as hepatolenticular degeneration as a result of accumulation of copper in the brain, liver, kidney and cornea due to its deranged biliary excretion1. In 1912, a WD was described as a familial syndrome of progressive lenticular degeneration associated with cirrhosis of the liver2. The etiological role of copper in the pathogenesis of WD was recognized much late

An automatic abstraction technique for verifying featured, parameterised systems

A general technique combining model checking and abstraction is presented that allows property based analysis of systems consisting of an arbitrary number of featured components. We show how parameterised systems can be specified in a guarded command form with constraints placed on variables which occur in guards. We prove that results that hold for a small number of components can be shown to scale up. We then show how featured systems can be specified in a similar way, by relaxing constraints on guards. The main result is a generalisation theorem for featured systems which we apply to two well known examples