ISSN:
1572-929X
Keywords:
Infinite-dimensional analysis
;
Schrödinger equation
;
Feynman–Kac formula
;
Wiener process
;
quantum field Hamiltonians
;
Heisenberg uncertainty principle.
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract Using the probabilistic Feynman–Kac formula, the existence of solutions of the Schrödinger equation on an infinite dimensional space E is proven. This theorem is valid for a large class of potentials with exponential growth at infinity as well as for singular potentials. The solution of the Schrödinger equation is local with respect to time and space variables. The space E can be a Hilbert space or other more general infinite dimensional spaces, like Banach and locally convex spaces (continuous functions, test functions, distributions). The specific choice of the infinite dimensional space corresponds to the smoothness of the fields to which the Schrödinger equation refers. The results also express an infinite-dimensional Heisenberg uncertainty principle: increasing of the field smoothness implies increasing of divergence of the momentum part of the quantum field Hamiltonian.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1008601707361
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