Finite approximations to quantum systems. (English) Zbl 0855.47046

The authors study quantum systems in finite-dimensional spaces as approximations to quantum systems in infinite-dimensional spaces. Numerical computations suggest that for a large class of Hamiltonians there exists a sequence of Hamiltonians in finite-dimensional space which spectral data converging in a very strong fashion to the spectral data of the Hamiltonian in infinite-dimensional space. The authors treat this problem for potentials which are positive, continuous and become infinite at infinite distances.


47N50 Applications of operator theory in the physical sciences
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
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