Solution of the Schrödinger Equation in the Hardy-Lebesgue Space
- 1 September 1971
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 12 (9) , 1961-1965
- https://doi.org/10.1063/1.1665830
Abstract
We present in this paper a uniform technique for the study of differential and difference equations in the Hardy‐Lebesgue space, i.e., the Hilbert space consisting of analytic functions in the unit disk, taking the Schrödinger equation as an example. The approach followed is based on the representation of the Hardy‐Lebesgue space by means of the unilateral shift operator, and reduces the problem of solving the Schrödinger equation to a perturbation problem of non‐self‐adjoint operators in an abstract separable Hilbert space.Keywords
This publication has 5 references indexed in Scilit:
- Abstract Formulation of the Quantum Mechanical Oscillator Phase ProblemJournal of Mathematical Physics, 1971
- Structure of the Point Spectrum of Schrödinger-Type Tridiagonal OperatorsJournal of Mathematical Physics, 1970
- Canonically Conjugate Pairs, Uncertainty Relations, and Phase OperatorsJournal of Mathematical Physics, 1970
- Spectral Theory of the Difference Equation f(n + 1) + f(n − 1) = [E − φ(n)]f(n)Journal of Mathematical Physics, 1969
- On the application of Bargmann Hilbert spaces to dynamical problemsAnnals of Physics, 1967