feat: Position & momentum unbounded operators#963
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gloges wants to merge 6 commits intolean-phys-community:masterfrom
Open
feat: Position & momentum unbounded operators#963gloges wants to merge 6 commits intolean-phys-community:masterfrom
gloges wants to merge 6 commits intolean-phys-community:masterfrom
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Continues on from #957 and makes progress on #851.
Introduces
schwartzEquiv, theLinearEquivbetween Schwartz functions and their image in the Hilbert space, along with some basic properties. This bijection is then used to define three symmetric unbounded operators with Schwartz submodule for domain, using the previously-defined continuous linear maps on Schwartz functions. These are the position and momentum unbounded operators, defined component-wise, and the (regularized) radius operator to any real power.There remains one sorry which will have to be revisited. Showing that the momentum operator on Schwartz functions is symmetric requires two results for
Space.deriv: integration-by-parts over all ofSpace dand commutation through complex conjugation.