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, Ψ0 = Ψ e iα , 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 Ψ0 = i ¯ h ∂ Ψ0 ∂t0 . 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 /λ-ft ) is an invariant. Recall the proof was for photons traveling
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