Confluent Supersymmetric Partners of Quantum Systems Emerging from the Spheroidal Equation
نویسندگان
چکیده
منابع مشابه
Confluent Supersymmetric Partners of Quantum Systems Emerging from the Spheroidal Equation
We construct confluent supersymmetric partners of quantum systems that emerge from the spheroidal equation. Properties of the systems and of their transformed counterparts are discussed.
متن کاملThe confluent algorithm in second order supersymmetric quantum mechanics
The confluent algorithm, a degenerate case of the second order supersymmetric quantum mechanics, is studied. It is shown that the transformation function must asymptotically vanish to induce non-singular final potentials. The technique can be used to create a single level above the initial ground state energy. The method is applied to the free particle, one-soliton well and harmonic oscillator.
متن کاملApplication of Heun’s Confluent Equation for the Solution of the Hydrogen Atom Problem in Spheroidal Coordinates
The Schrödinger equation in prolate spheroidal coordinates separates into ordinarydifferential equations in single coordinates; of these direct solutions, two contain confluent Heun functions. We derive polynomial solutions of Heun’s confluent equation and express Coulomb spheroidal functions in a closed algebraic form. Spheroidal orbitals are expressible as hybrids composed of spherical ones c...
متن کاملSupersymmetric Biorthogonal Quantum Systems
We discuss supersymmetric biorthogonal systems, with emphasis given to the periodic solutions that occur at spectral singularities of PT symmetric models. For these periodic solutions, the dual functions are associated polynomials that obey inhomogeneous equations. We construct in detail some explicit examples for the supersymmetric pairs of potentials V± (z) = −U (z) 2 ±z d dz U (z) where U (z...
متن کاملSupersymmetric Quantum Mechanics and Painlevé IV Equation
As it has been proven, the determination of general one-dimensional Schrödinger Hamiltonians having third-order differential ladder operators requires to solve the Painlevé IV equation. In this work, it will be shown that some specific subsets of the higher-order supersymmetric partners of the harmonic oscillator possess third-order differential ladder operators. This allows us to introduce a s...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Symmetry
سال: 2015
ISSN: 2073-8994
DOI: 10.3390/sym7020412