rigged Hilbert space
In extensions of Quantum Mechanics [1, 2], the concept of rigged Hilbert spaces allows one “to put together” the discrete spectrum of eigenvalues corresponding to the bound states (eigenvectors) with the continuous spectrum (as , for example, in the case of the ionization of an atom or the photoelectric effect).
A rigged Hilbert space is a pair with a Hilbert space and is a dense subspace with a topological vector space structure for which the inclusion map is continuous. Between and its dual space there is defined the adjoint map of the continuous inclusion map . The duality pairing between and also needs to be compatible with the inner product on :
whenever and .
- 1 R. de la Madrid, “The role of the rigged Hilbert space in Quantum Mechanics.”, Eur. J. Phys. 26, 287 (2005); .
- 2 J-P. Antoine, “Quantum Mechanics Beyond Hilbert Space” (1996), appearing in Irreversibility and Causality, Semigroups and Rigged Hilbert Spaces, Arno Bohm, Heinz-Dietrich Doebner, Piotr Kielanowski, eds., Springer-Verlag, .
|Title||rigged Hilbert space|
|Date of creation||2013-03-22 19:22:48|
|Last modified on||2013-03-22 19:22:48|
|Last modified by||bci1 (20947)|
|Defines||dual Hilbert space|