This preview shows page 1. Sign up to view the full content.
Unformatted text preview: i.e. orthonormal like the discrete solutions < n  m >= nm ). Most General Solution: The most general solution is a superposition of the free particle eigenfunctions as follows + + = = dk e k f dk t x k f t x t k kx i k ) ) ( ( ) ( 2 1 ) , ( ) ( ) , ( , where ) 2 /( ) ( 2 m k k h = . The dependence of on k is called the dispersion . The coefficient function f(k) (analogous to the overlap constants c n =< n  >) is given by + = dx e x k f ikx ) , ( 2 1 ) ( . Fourier Transforms: f(k) is the Fourier transform of F(x) and F(x) is the inverse Fourier transform of f(k) as follows: + = dk e k f x F ikx ) ( 2 1 ) ( + = dx e x F k f ikx ) ( 2 1 ) (...
View
Full
Document
This note was uploaded on 05/29/2011 for the course PHY 4064 taught by Professor Fields during the Spring '07 term at University of Florida.
 Spring '07
 FIELDS
 mechanics, Energy

Click to edit the document details