8 papers
Exactly solvable Schrödinger operators related to the hypergeometric equation
Jan DereziÅski, Pedram Karimi
We study one-dimensional Schrödinger operators defined as closed operators that are exactly solvable in terms of the Gauss hypergeometric function. We allow the potentials to be c…
Confluent functions, Laguerre polynomials and their (generalized) bilinear integrals
Jan DereziÅski, Christian GaÃ, Joonas Mikael Vättö
We review properties of confluent functions and the closely related Laguerre polynomials, and determine their bilinear integrals. As is well-known, these integrals are convergent o…
Propagators in curved spacetimes from operator theory
Jan DereziÅski, Christian GaÃ
We discuss two distinct operator-theoretic settings useful for describing (or defining) propagators associated with a scalar Klein-Gordon field on a Lorentzian manifold . Typica…
A unified approach to hypergeometric class functions
Jan DereziÅski
Hypergeometric class equations are given by second order differential operators in one variable whose coefficient at the second derivative is a polynomial of degree , at the…
Exactly solvable Schrödinger operators related to the confluent equation
Jan DereziÅski, Jinyeop Lee
Our paper investigates one-dimensional Schrödinger operators defined as closed operators on or that are exactly solvable in terms of confluen…
Axial anomaly in the presence of arbitrary spinor interactions
Jan DereziÅski, Adam LatosiÅski
We consider N Dirac fermions on a 4-dimensional Euclidean space with a quadratic interaction given by arbitrary external Clifford-valued fields. The divergence of the axial current…