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Unformatted text preview: 56. (a) Using Euler’s formula eiφ = cos φ + i sin φ, we rewrite ψ(x) as ψ ( x ) = ψ 0 eikx = ψ 0 ( cos kx + i sin kx ) = (ψ 0 cos kx ) + i (ψ 0 sin kx ) = a + ib,
where a =ψ0 cos kx and b = ψ0 sin kx are both real quantities.
(b) The time-dependent wave function is ψ ( x , t ) = ψ ( x )e − iωt = ψ 0eikx e −iωt = ψ 0ei ( kx −ωt )
= [ψ 0 cos( kx − ωt )] + i[ψ 0 sin( kx − ωt )]. ...
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This note was uploaded on 06/03/2011 for the course PHY 2049 taught by Professor Any during the Spring '08 term at University of Florida.
- Spring '08