assignment10

assignment10 - Problem Set 10 Note: This problem set is due...

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Problem Set 10 Note: This problem set is due Nov 22 before midnight. Please leave it in my mailbox located at the Frst ±oor of Rutherford building. 1. Imagine I form a wavepacket for a free particle of mass m using only three plane waves of momenta k 0 , k 0 - Δ k 2 and k 0 + Δ k 2 with amplitudes proportional to 1 , 1 2 and 1 2 respectively. Find the form of the wavepacket at time t = 0. Using a reasonable de±nation of Δ x , show that Δ x Δ k 4 π. (1) Find also the time evolution of the system and determine the peak of the wavepacket at a time t . How will the result change if the three waves were electromagnetic? 2. A neutron is emitted from a furnace at a temperature 300 K . What is the de-Broglie wavelength of the neutron? If I want the same wavelength for an electron, how much potential di²erence (in volts) should I accelerate the electron through? You will ±nd that for smaller wavelengths, we require higher energies. Therefore in some regime non- relativistic analysis can no longer hold. Can you calculate the de-Broglie wavelength of an
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This note was uploaded on 02/20/2011 for the course PHYS 357 taught by Professor Keshavdasgupta during the Fall '05 term at McGill.

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assignment10 - Problem Set 10 Note: This problem set is due...

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