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 = − h and hence ikx Ae x = ) ( where A is a constant and E m k = ) 2 /( 2 2 h . The state ψ (x) has k p x h >= < and 2 2 2 k p x h >= < which means Δ 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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 Spring '07
 FIELDS
 mechanics, Energy, Potential Energy, Schrodinger Equation, Quantum Mechanical Hamiltonian operator

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