Unformatted text preview: emitted and absorbed. 2. Assumes that all relevant velocities are much less than the speed of light ( i.e. nonrelativistic). Free Particle: A free particle ( i.e. V(x) = 0) with energy E must satisfy ) ( ) ( 2 2 2 2 x E dx x d m Φ = Φ − h and hence ikx Ae x = Φ ) ( where A is a constant and E m k = ) 2 /( 2 2 h . The state Φ (x) has k p x h >= < and 2 2 2 k p x h >= < which means ∆ p x = 0 ( i.e. no uncertainty in p x ). Thus, ) ( ) , ( t kx i Ae t x ω − = Ψ corresponds to a free particle with definite momentum k p x h = and definite energy h = E , but the position of the particle is completely uncertain ( i.e. the particle is equally likely to be anywhere)....
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This note was uploaded on 05/29/2011 for the course PHY 3063 taught by Professor Field during the Spring '07 term at University of Florida.
 Spring '07
 Field
 Physics, Energy, Potential Energy

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