Exactly solvable Schrödinger operators

Abstract

We systematically describe and classify 1-dimensional Schrödinger equations that can be solved in terms of hypergeometric type functions. Beside the well-known families, we explicitly describe 2 new classes of exactly solvable Schrödinger equations that can be reduced to the Hermite equation.

20 pages, v2

References in corpus (1)

• Shape invariant hypergeometric type operators with application to quantum mechanics

Cited by in corpus (23)

• Quantum mechanics without potential function
• Potentials of the Heun class
• New conditionally exactly solvable inverse power law potentials
• Potentials of the Heun class: the triconfluent case
• Rational extension and Jacobi-type {\boldmath{$X_m$}} solutions of a quantum nonlinear oscillator
• Renormalization of the strongly attractive inverse square potential: Taming the singularity
• Liouville transformations and quantum reflection
• Third-order ladder operators, generalized Okamoto and exceptional orthogonal polynomials
• Bessel-Type Operators and a refinement of Hardy's inequality
• Continuous and holomorphic functions with values in closed operators
• Green's functions and the Cauchy problem of the Burgers hierarchy and forced Burgers equation
• Waves in the Witten Bubble of Nothing and the Hawking Wormhole
• Scarf for Lifshitz
• Quantum particle in a spherical well confined by a cone
• Propagators in curved spacetimes from operator theory
• Pseudo-Hermitian and PT -symmetric quantum systems with energy-dependent potentials: Bound-state solutions and energy spectra
• Multichannel Framework for Singular Quantum Mechanics
• Classical probability density distributions with uncertainty relations for ground states of simple non-relativistic quantum-mechanical systems
• Recurrence Relations for Finite-Temperature Correlators via AdS${}_2$/CFT${}_1$
• Heat Kernel on Warped Products
• Exactly solvable Schrödinger operators related to the confluent equation
• The exotic structure of the spectral $\zeta$-function for the Schrödinger operator with Pöschl--Teller potential
• A comparison of the Georgescu and Vasy spaces associated to the N-body problems and applications