PS1_2011 - Use the definitions of partial derivatives in...

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ME 6700 Carbon Nanotube Science and Technology Problem Set 1: Basics of quantum mechanics Due Date: September 21, 2011 1. For an 1D particle in a box, calculate: for the two lowest-energy eigenstates. Then calculate and compare to the minimum set by the Heisenberg principle 2. Angular momentum operators: the angular momentum is defined as: a. In spherical coordinates, the z component and magnitude squared become:
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Unformatted text preview: Use the definitions of partial derivatives in spherical coordinates, shown below, to verify the formula for L z b. Using the definitions of the spherical harmonics, verify that: for ( l,m ) = (1,1) and (1,0) 3. P orbitals: Make a 2D surface plot (i.e. magnitude vs. x,y) of the p x orbital on the x-y plane for n = 2. You can use any graphing software like Matlab or MS-Excel....
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PS1_2011 - Use the definitions of partial derivatives in...

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