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Unformatted text preview: (scalar product) is an integral. For example, the collection of all complex functions f(x) of a real variable x with period 2 π forms a complex vector space. Define the inner (scalar) product by &lt;f(x)|g(x)&gt;= dx x g x f ) ( ) ( * ∫ − π a. Show that D=-id/dx is a Hermitian operator on this space. What are its eigenvalues and normalized eigenvectors? b. What are the eigenvalues and eigenvectors of D 2 =-d 2 /dx 2 ? c. Define the reflection operator R on this space by Rf(x)=f(-x) . Show that the commutator [ R,D ] ≠ 0. What is [ R,D 2 ]?...
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This note was uploaded on 10/11/2009 for the course PHYSICS 866 taught by Professor Js during the Spring '08 term at Pohang University of Science and Technology.
- Spring '08