integrable schrodinger operators with magnetic fields factorization method on curved surfaces the factorization method for schrodinger operators with magnetic fields on a two dimensional surface m2 with nontrivial metric is investigated this leads to the new integrable examples of such operators and brings a new look at some classical problems such as the dirac magnetic monopole and the landau problem the global geometric aspects and related spectral properties of the operators from the factorization chains are discussed in detail we also consider the laplace transformations on a curved surface and extend the class of schrodinger operators with two integrable levels introduced in the flat case by s p novikov and one of the authors

non self adjoint hamiltonians defined by riesz bases we discuss some features of non self adjoint hamiltonians with real discrete simple spectrum under the assumption that the eigenvectors form a riesz basis of hilbert space among other things we give conditions under which these hamiltonians can be factorized in terms of generalized lowering and raising operators

recurrence approach and higher rank cubic algebras for the n dimensional superintegrable systems by applying the recurrence approach and coupling constant metamorphosis we construct higher order integrals of motion for the stackel equivalents of the n dimensional superintegrable kepler coulomb model with non central terms and the double singular oscillators of type n n n we show how the integrals of motion generate higher rank cubic algebra c 3 circle plus l 1 circle plus l 2 with structure constants involving casimir operators of the lie algebras l 1 and l 2 the realizations of the cubic algebras in terms of deformed oscillators enable us to construct finite dimensional unitary representations and derive the degenerate energy spectra of the corresponding superintegrable systems

appearances of pseudo bosons from black scholes equation it is a well known fact that the black scholes equation admits an alternative representation as a schrodinger equation expressed in terms of a non self adjoint hamiltonian we show how pseudo bosons linear or not naturally arise in this context and how they can be used in the computation of the pricing kernel

two families of superintegrable and isospectral potentials in two dimensions as an extension of the intertwining operator idea an algebraic method which provides a link between supersymmetric quantum mechanics and quantum super integrability is introduced by realization of the method in two dimensions two infinite families of superintegrable and isospectral stationary potentials are generated the method makes it possible to perform darboux transformations in such a way that in addition to the isospectral property they acquire the superintegrability preserving property symmetry generators are second and fourth order in derivatives and all potentials are isospectral with one of the smorodinsky winternitz potentials explicit expressions of the potentials their dynamical symmetry generators and the algebra they obey as well as their degenerate spectra and corresponding normalizable states are presented

intertwining operators for non self adjoint hamiltonians and bicoherent states this paper is devoted to the construction of what we will call exactly solvable models i e of quantum mechanical systems described by an hamiltonian h whose eigenvalues and eigenvectors can be explicitly constructed out of some minimal ingredients in particular motivated by pt quantum mechanics we will not insist on any self adjointness feature of the hamiltonians considered in our construction we also introduce the so called bicoherent states we analyze some of their properties and we show how they can be used for quantizing a system some examples both in finite and in infinite dimensional hilbert spaces are discussed

two dimensional magnetic schrodinger equations darboux transformations and solutions of associated auxiliary equations we extend the formalism of darboux transformations to magnetic schrodinger equations in two dimensions the partner potentials associated with the darboux transformation are obtained in explicit form through an integral formula we apply our construction to a particular spectral problem of dirichlet type obtaining the darboux partner its spectrum and the corresponding solutions in explicit form

more mathematics for pseudo bosons we propose an alternative definition for pseudo bosons this simplifies the mathematical structure minimizing the required assumptions some physical examples are discussed as well as some mathematical results related to the biorthogonal sets arising out of our framework we also briefly extend the results to the so called nonlinear pseudo bosons

group theory of the smorodinsky winternitz system the three degrees of freedom smorodinsky winternitz system is a degenerate or super integrable hamiltonian that possesses five functionally independent globally defined and single valued integrals of the motion in both classical and quantum mechanics this is explained in terms of a forced degeneracy imposed as a consequence of the invariance of the hamiltonian under a group of symmetry transformations isomorphic to the three dimensional unitary unimodular group su 3 in turn this degeneracy group is embedded in a larger group of transformations that maps all the bound energy levels among each other the so called dynamical group all the bound state eigenfunctions act as basis functions for a single irreducible representation of the dynamical group so in common with the hydrogen atom and the harmonic oscillator the quantum mechanics of the smorodinsky winternitz system may be completely solved within the framework of group theory alone

quadratic poisson algebras of two dimensional classical superintegrable systems and quadratic associative algebras of quantum superintegrable systems the integrals of motion of the classical two dimensional superintegrable systems with quadratic integrals of motion close in a restrained quadratic poisson algebra whose the general form is investigated each classical superintegrable problem has a quantum counterpart a quantum superintegrable system the quadratic poisson algebra is deformed into a quantum associative algebra the finite dimensional representations of this algebra are calculated by using a deformed parafermion oscillator technique it is shown that the finite dimensional representations of the quadratic algebra are determined by the energy eigenvalues of the superintegrable system the calculation of energy eigenvalues is reduced to the solution of algebraic equations which are universal that is for all two dimensional superintegrable systems with quadratic integrals of motion

combined state adding and state deleting approaches to type iii multi step rationally extended potentials applications to ladder operators and superintegrability type iii multi step rationally extended harmonic oscillator and radial harmonic oscillator potentials characterized by a set of k integers m1 m2 mk such that m1 m2 mk with mi even resp odd for i odd resp even are considered the state adding and state deleting approaches to these potentials in a supersymmetric quantum mechanical framework are combined to construct new ladder operators the eigenstates of the hamiltonians are shown to separate into mk 1 infinite dimensional unitary irreducible representations of the corresponding polynomial heisenberg algebras these ladder operators are then used to build a higher order integral of motion for seven new infinite families of superintegrable two dimensional systems separable in cartesian coordinates the finite dimensional unitary irreducible representations of the polynomial algebras of such systems are directly determined from the ladder operator action on the constituent one dimensional hamiltonian eigenstates and provide an algebr

superintegrability and higher order polynomial algebras we present a method to obtain higher order integrals and polynomial algebras for two dimensional quantum superintegrable systems separable in cartesian coordinates from ladder operators all systems with a second and a third order integral of motion separable in cartesian coordinates were studied the integrals of motion of two of them do not generate a cubic algebra we construct for these hamiltonians a higher order polynomial algebra from their ladder operators we obtain quintic and seventh order polynomial algebras we also give for the polynomial algebras of order 7 realizations in terms of deformed oscillator algebras these realizations and finite dimensional unitary representations allow us to obtain the energy spectrum we also apply the construction to the caged anisotropic harmonic oscillator and a system involving the fourth painleve transcendent

intertwining operators for solving differential equations with applications to symmetric spaces the use of intertwining operators to solve both ordinary and partial differential equations is developed classes of intertwining operators are constructed which transform between laplacians which are self adjoint with respect to different non trivial measures in the two dimensional case the intertwining operator transforms a non separable partial differential operator to a separable one as an application the heat kernels on the rank 1 and rank 2 symmetric spaces are constructed

new ladder operators for a rational extension of the harmonic oscillator and superintegrability of some two dimensional systems new ladder operators are constructed for a rational extension of the harmonic oscillator associated with type iii hermite exceptional orthogonal polynomials and characterized by an even integer m the eigenstates of the hamiltonian separate into m 1 infinite dimensional unitary irreducible representations of the corresponding polynomial heisenberg algebra these ladder operators are used to construct a higher order integral of motion for two superintegrable two dimensional systems separable in cartesian coordinates the polynomial algebras of such systems provide for the first time an algebraic derivation of the whole spectrum through their finite dimensional unitary irreducible representations

scale properties of the seismic wavefield perspectives for full waveform matching starting from the nondimensionalization of equations of motion we partition the set of the velocity models in equivalence classes such that the full waveform of an element in a given class can be calculated from the full waveform of any other element in the same class by scaling model parameters we give a formal derivation of the seismic wavefield scale properties and we prove their capability through the use of numerical examples besides this we introduce how the scale properties can be used to save computational time in full waveform modeling and inversion in forward modeling we can use them for the calculation of the full waveform of any model in the same equivalence class of a model whose full waveform has been previously calculated in full waveform inversion scale properties can be used for full waveform matching given an experimental seismogram and a synthetic one we can choose in the same class of the synthetic model another element whose waveform is closer to the experimental one

darboux transformations for schrodinger equations in two variables darboux transformations in one variable form the basis for the factorization methods and have numerous applications to geometry nonlinear equations and susy quantum mechanics in spite of this wide range of applications the theory of darboux transformations in two variables and its elegant relationship to analytic complex functions has not been recognized in the literature to close this gap we develop in this paper the theory of darboux transformation in the context of schrodinger equations in two variables this yields a constructive algorithm to determine the relationship between potential functions which are related by darboux transformations

some invariant biorthogonal sets with an application to coherent states abstract we show how to construct out of a certain basis invariant under the action of one or more unitary operators a second biorthogonal set with similar properties in particular we discuss conditions for this new set to be also a basis of the hilbert space and we apply the procedure to coherent states we conclude the paper considering a simple application of our construction to pseudo hermitian quantum mechanics

on form preserving transformations for the time dependent schrodinger equation in this paper we point out a close connection between the darboux transformation and the group of point transformations which preserve the form of the time dependent schrodinger equation tdse in our main result we prove that any pair of time dependent real potentials related by a darboux transformation for the tdse may be transformed by a suitable point transformation into a pair of time independent potentials related by a usual darboux transformation for the stationary schrodinger equation thus any real potential solvable via a time dependent darboux transformation can alternatively be solved by applying an appropriate form preserving point transformation of the tdse to a time independent potential the pre eminent role of the latter type of transformations in the solution of the tdse is illustrated with a family of quasi exactly solvable time dependent anharmonic potentials

higher order darboux transformations in two dimensions linearizable auxiliary equations and invariant potentials we show that the two dimensional schrodinger equation admits darboux transformations only for a particular class of potentials it is demonstrated that for such potentials the associated auxiliary equation can be linearized to schrodinger form furthermore since the aforehand mentioned class of potentials turns out to remain invariant under darboux transformations construction of multiple higher order darboux transformations chains becomes possible we present second order chains in explicit form and give an algorithmic scheme for the construction of higher order chains

regular pseudo bosons versus bosons we discuss in which sense the so called regular pseudo bosons recently introduced by trifonov and analyzed in some detail by the author are related to ordinary bosons we repeat the same analysis for pseudo bosons and analyze the role played by certain intertwining operators which may be bounded or not

darboux transformations for 1 2 dimensional fokker planck equations with constant diffusion matrix we construct a darboux transformation for 1 2 dimensional fokker planck equations with constant diffusion matrix our transformation is based on the two dimensional supersymmetry formalism for the schrodinger equation the transformed fokker planck equation and its solutions are obtained in explicit form

superintegrable n 2 systems quadratic constants of motion and potentials of drach the properties of superintegrable systems in two degrees of freedom possessing three independent globally defined constants of motion are studied using as an approach the existence of hidden symmetries and the generalized noether s theorem the potentials are obtained as solution of a system of two partial differential equations first the case of standard lagrangians is studied and then the method is applied to the case of lagrangians with a pseudo euclidean kinetic term finally the results are related with other approaches and with a family of potentials admitting a second integral of motion cubic in the velocities obtained by drach

gibbs states defined by biorthogonal sequences motivated by the growing interest in pt quantum mechanics in this paper we discuss some facts on generalized gibbs states and their related kms like conditions to achieve this we first consider some useful connections between similar hamiltonian operators and we propose some extended versions of the heisenberg algebraic dynamics deducing some of their properties that are useful for our purposes

positive solutions for logistic type quasilinear elliptic equations on rn in this paper we consider positive solutions of the logistic type p laplacian equation pu a x u p 2u b x u q 1u x rn n 2 we show that under rather general conditions on a x and b x for large x the behavior of the positive solutions for large x can be determined this is then used to show that there is a unique positive solution our results improve the corresponding ones in j london math soc 2 64 2001 107 124 and j anal math in press

intertwined isospectral potentials in an arbitrary dimension the method of intertwining with n dimensional nd linear intertwining operator l is used to construct nd isospectral stationary potentials it has been proven that the differential part of l is a series in euclidean algebra generators integrability conditions of the consistency equations are investigated and the general form of a class of potentials respecting all these conditions have been specified for each n 2 3 4 5 the most general forms of 2d and 3d isospectral potentials are considered in detail and construction of their hierarchies is exhibited the followed approach provides coordinate systems which make it possible to perform separation of variables and to apply the known methods of supersymmetric quantum mechanics for 1d systems it has been shown that in choice of coordinates and l there are a number of alternatives increasing with n that enlarge the set of available potentials some salient features of higher dimensional extension as well as some applications of the results are presented

intertwining relations of non stationary schrodinger operators general first and higher order intertwining relations between non stationary one dimensional schrodinger operators are introduced for the first order case it is shown that the intertwining relations imply some hidden symmetry which in turn results in an r separation of variables the fokker planck and diffusion equations are briefly considered second order intertwining operators are also discussed within a general approach however due to its complicated structure only particular solutions are given in some detail

exact solvability of superintegrable systems it is shown that all four superintegrable quantum systems on the euclidean plane possess the same underlying hidden algebra sl 3 the gauge rotated hamiltonians as well as their integrals of motion once rewritten in appropriate coordinates preserve a flag of polynomials this flag corresponds to highest weight finite dimensional representations of the sl 3 algebra realized by first order differential operators