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hw1 - Name ID Assignment#1 PHYS-446 due in cla ss on 19...

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Name:_________________ ID:_________________ Assignment #1 PHYS-446 due in class on 19 September 2008 1. (a) Calculate your de Broglie wavelength as you walk down Milton street. Assume some realistic values of the quantities you need. How small (width) would a door have to be for you to display wave behaviour (such as diffraction) as you “squeeze” through this door (if you could...). (b) How fast would you have to go in order to have a de Broglie wavelength that could potentially be measured experimentally, let's say of order 1 μm ? 2. Given the following wavefunction of an electron:  x ,t = Ae m 2 x 2 e i t 2 where A ,m , are real constants. Show that the wavefunction satisfies Schroedinger's equation with a potential of the form V x = 1 2 m 2 x 2 . 3. Given the following wavefunction of an electron:  x ,t = 2 a sin 2 a x e iEt / where a , E are positive real constants. (a) Sketch the wavefunction in the region 0 x a at t = 0.
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