hw3_p5405_f01 - HW Phys5405 f01 due Oct. 18,2001 2 h 1)...

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HW Phys5405 f01 due Oct. 18,2001 1) Show that the Schrodinger Equation, - ¯ h 2 2 m 2 Ψ = i ¯ h Ψ ∂t , is invariant under the Galillean transform, provided the wave function in the O’ frame is renormalized by a phase, Ψ 0 = Ψ e , where α = - mv ¯ h ( z - vt/ 2) and z is the direction of relative motion between O and O’. That is, show that - ¯ h 2 2 m 0 2 Ψ 0 = i ¯ h Ψ 0 ∂t 0 . 2) JDJ 11-4 (hint - use length contraction) 3) Use the results from the derivation of the Doppler shift, as done in class, to show that the phase of a wave, 2 π ( n · r - ft ) is an invariant. Recall the proof was for photons traveling
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This note was uploaded on 12/24/2011 for the course PHYS 5406 taught by Professor Blecher during the Spring '10 term at Virginia Tech.

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