I got curious while studying quantum mechanics. Suppose we have two self-adjoint operators $A$ and $B$ and let's say they do commute as well. Let $\sigma(A)$ be a pure point spectrum of $A$ and $\sigma(B)$ be singular (or absolute) continuous spectrum of $B$. Then what is a spectrum of $A + B$? Is it singular (or absolute) continuous? Or pure point spectrum? What do you think? It would be a great help if relevant references are provided, if you know any. Thanks : )
2026-02-23 20:42:03.1771879323
Spectrum of sum of two commuting self-adjoint operators with different spectrum classification
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