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Unformatted text preview: P460  math concepts 1 General Structure of Wave Mechanics (Ch. 5) Sections 51 to 53 review items covered previously use Hermitian operators to represent observables (H,p,x) eigenvalues of Hermitian operators are real and give the expectation values eigenvectors for different eigenvalues are orthogonal and form a complete set of states any function in the space can be formed from a linear series of the eigenfunctions some variables are conjugate (position, momentum) and one can transform from one to the other and solve the problem in eithers space x d x i dx p p e x u C t x product dot dx u u u u j i x u ions eigenfunct op iEt N N ij j i j i i ) ( ) ( ) , (   ) ( : * * / * = >= < = = >= >=< < h h P460  math concepts 2 Notation there is a very compact format (Dirac notation) that is often used i> = u i > = eigenfunction < > is a dot product between 2 function i><j is an outer product (a matrix). For example a rotation between two different basis if an index is repeated there is an implied sum operator projection n n n n n C x u C x product dot dx u u u u j i x u ions eigenfunct N N N ij j i j i i = = = = >= >=< < ) ( ) (   ) ( : * P460  math concepts 3 Degeneracy (Ch. 54) If two different eigenfunctions have the same eigenvalue they...
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This note was uploaded on 10/02/2009 for the course PHYS 460 taught by Professor Johnson,c during the Spring '08 term at Northern Illinois University.
 Spring '08
 Johnson,C
 mechanics, Quantum Physics

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