Kato's Perturbation Theory is a mathematical framework used to analyze how small changes or 'perturbations' in an operator affect the spectral properties of a quantum system. This theory is particularly important for understanding the resolvent of operators, which provides insights into the eigenvalues and eigenfunctions under perturbations. By focusing on the resolvent, Kato's theory connects the stability of spectral properties to perturbations in the Hamiltonian, enabling deeper insights into quantum mechanics.
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