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Hilbert Spaces and Linear Operators

Algebra & topology, linear operator theory & spectral theory. Dirac notation.

Dirac Notation — Infinite Dimension

Hilbert representation of point-particle quantum mechanics, position and momentum operators, and Dirac delta.

Dirac notationInfinite dimensionPosition representationMomentum representationDirac deltaFourier transformResolution of identityPosition operatorMomentum operatorCanonical commutation

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Lesson 4: Linear Operator Theory
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Lesson 6: Bounded Operators