Unformatted text preview: would be found outside the well ( x > a )? 3. (a) Show that Ψ( x,t ) = ± mω π ¯ h ¶ 1 / 4 exp (mω 2¯ h " x 2 + a 2 2 ‡ 1 + ei 2 ωt · + i ¯ ht m2 axeiωt #) satisﬁes the timedependent Schr¨odinger equation for the harmonic oscillator potential. Here a is any real constant with the dimensions of length. (b) Find  Ψ ( x,t )  2 , and describe the motion of the wave packet. (c) Compute h x i and h p i , and check that Ehrenfest’s theorem is satisﬁed: m d dt h x i = h p i and d dt h p i =h dV dx i . —— End ——...
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 Spring '11
 CFLO
 Energy, Kinetic Energy, Potential Energy, kinetic energy operator, highestenergy bound state, timedependent schr¨dinger equation, potential energy operator, —— End ——

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