Infinite dimensional fock spaces and schrödinger equation solutions

Abstract

A scale of infinite dimensional Fock spaces, r^PB =U r^P,sB is introduced having many fundamental properties. Each space, r^PsB , is a Frechet space. A generalized Laplacian is introduced whereby a space, r^P,sB , is transformed into a space, r ^P,s'B The components of the vector representing a point in r^P,sB have tempered distributions as theirdomain thus generalizing similar construction within Hilbert spaces. An infinite dimensional Schrodinger equation is investigated within the context of this Fock space. An explicit algorithm computing the solution to it is proven and uniqueness is also shown. The spirit of the algorithm is in the context of an operational calculus.

Keywords:

• Fock spaces
• Schrödinger equation

Keywords:

• 35K22