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20112ee2_1_EE2 HW1

20112ee2_1_EE2 HW1 - n y n z respectively If there are 7...

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EE2 11S HW1 Due April 14, 2011 Problem#1 (30 points) a) Calculate the de Broglie wavelength of a particle with mass equal to 1.5 g and moving with a velocity of 10 km per hour. b) For electrons which are excited across a voltage of 50-400 Volts, calculate the range of the de Broglie wavelengths. Problem#2 (30points) Consider an electron in an infinite potential box of dimensions 1nm × 2nm × 4nm. Determine the components of momentum (p x , p y , p z ) and the total kinetic energy of the state with quantum numbers (2, 3, 2) for (n x
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Unformatted text preview: , n y , n z ), respectively. If there are 7 electrons inside of this box, what’s the highest electron energy? (Taking spin into consideration, in each state the maximum electrons are 2.) Problem #3 (40points) Define 2 2-A A A ∆ = < < Consider a Gaussian wavepacket with an initial state 2 2-ik-x /4 ( , 0) x a x t Be e ψ = = Use the normalization relation to find B. Calculate the momentum uncertainty p ∆ at t =0 and the position uncertainty x ∆ . Show that these obey Heisenberg’s uncertainty principle....
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