Abstract
We have seen in “Lecture 5: Automorphisms; Quantum Dynamics; Theorems of Wigner, Kadison, Segal; Continuity and Generators” that when \(V\) is bounded Duhamel’s formula can be used to prove that the operator \( - \varDelta + V(x) , x \in R^d \) is self-adjoint and therefore it is the generator of a unitary group of operators.
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References
Akhiezer, N., & Glazman, I. (1963). Theory of linear opertors in Hilbert space (Vols. I, II). New York: Frederick Ungar Publisher Co. (F. Ungar ed., 1961).
Albeverio, A., Gesztesy, F., Hoegh-Kroen, R., & Holden, H. (1988). Solvable models in quantum mechanics, New York: Springer.
Faddaev, L. (1965). Mathematical aspects of the three-body problem. New York: Daniel Davey & Co.
Kato, T. (1980). Perturbation theory for linear operators. New York: Springer.
Reed, M., & Simon, B. (1975). Method of mathematical physics (Vols. I, II, IV). London: Academic Press.
Yoshida, K. (1971). Functional analysis. New York: Springer.
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Dell’Antonio, G. (2015). Lecture 17: Kato-Rellich Comparison Theorem. Rollnik and Stummel Classes. Essential Spectrum. In: Lectures on the Mathematics of Quantum Mechanics I. Atlantis Studies in Mathematical Physics: Theory and Applications, vol 1. Atlantis Press, Paris. https://doi.org/10.2991/978-94-6239-118-5_17
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DOI: https://doi.org/10.2991/978-94-6239-118-5_17
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