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This 7 page Class Notes was uploaded by Citlalli Sauer on Tuesday October 20, 2015. The Class Notes belongs to PHYS410 at San Diego State University taught by Staff in Fall. Since its upload, it has received 51 views. For similar materials see /class/225321/phys410-san-diego-state-university in Physics 2 at San Diego State University.
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Date Created: 10/20/15
Lecture 22 Outline Hilbert Space QUIZ TIME 0 back to vector spaces Section A1 re ux a into Hilbert space Section 31 Functions as Vectors o D0 problem A2 contd In the beginningHillbilly space a The set of all functions f forms a vector space Restrict to normalizable physical states f ib2das l b fa such that f12 da lt 00 which constitutes the L2a b or Hilbert space De ning the inner product of two functions as ltfggt fltxgtgltxgtdx QM restrict to normalizable physical states This de nition satis es the inner product requirements Inner products Given ltfggt fagada then we ltglfgt ltflggt and ltffgt f fltxgtl2dx a function is normalised if lt f f gt l a set of functions are orthonormal if ltf fjgt 6 a set of functions fna are complete if for all OTHER functions 95 937 ggt Remember to determine on use Fourier s trick on fxgxdx ltnt9gt Vector Space Example a Problem 31 on the board Vector Space Example a Problem 32 on the board
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