The Rigged Hilbert Space of the Free Hamiltonian

Abstract

We explicitly construct the Rigged Hilbert Space (RHS) of the free Hamiltonian $H_0$. The construction of the RHS of $H_0$ provides yet another opportunity to see that when continuous spectrum is present, the solutions of the Schrodinger equation lie in a RHS rather than just in a Hilbert space.

arXiv comment18 pages. Invited, refereed contribution to the Jaca proceedings; v2: minor, cosmetic changes

References in corpus (3)

• Rigged Hilbert Space Treatment of Continuous Spectrum
• Rigged Hilbert Space Approach to the Schrodinger Equation
• Formal and Precise Derivation of the Green Functions for a Simple Potential

Cited by in corpus (10)

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• Observables in Quantum Mechanics and the Importance of Self-adjointness
• Relativistic free motion time of arrival operator for massive spin-0 particles with positive energy
• The rigged Hilbert space approach to the Lippmann-Schwinger equation. Part I
• The rigged Hilbert space approach to the Lippmann-Schwinger equation. Part II: The analytic continuation of the Lippmann-Schwinger bras and kets
• Reply to ``Comment on `On the inconsistency of the Bohm-Gadella theory with quantum mechanics'''