MidtermExample1

MidtermExample1 - MIDTERM EXAMPLE 1 SI-MKS 8 Speed of light...

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Applied quantum mechanics MIDTERM EXAMPLE 1 SI-MKS Speed of light in free space Planck’s constant Electron charge Electron mass Neutron mass Proton mass Boltzmann constant Permittivity of free space Permeability of free space Speed of light in free space Avagadro’s number Bohr radius Inverse fine-structure constant c 2.99792458 10 8 × m s 1 = h 6.5821188926 10 16 × eV s = h 1.054571596 10 34 × J s = e 1.602176462 10 19 × C = m 0 9.10938188 10 31 × kg = m n 1.67492716 10 27 × = m p 1.67262158 10 27 × = k B 1.3806503 10 23 × J K 1 = k B 8.617342 10 5 × eV K 1 = ε 0 8.8541878 10 12 × F m 1 = µ 0 4 π 10 7 × H m 1 = c 1 ε 0 µ 0 = N A 6.02214199 10 23 × mol 1 = a B 0.52917721 10 × 10 m = a B 4 πε 0 h 2 m 0 e 2 ---------------- = α 1 137.0359976 = α 1 4 0 h c e 2 ----------------- =
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PROBLEM 1 Consider a particle mass m and charge e moving in the one-dimensional periodic poten- tial V ( x ) sketched in the following figure. (a) Assuming periodic boundary conditions are applied to the potential defined in the region , what is the value of k for the 1-st (lowest) energy eigenvalue and what is the value of k for the 8-th energy eigenvalue?
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This note was uploaded on 02/01/2009 for the course EE 539 taught by Professor Levi during the Fall '06 term at USC.

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MidtermExample1 - MIDTERM EXAMPLE 1 SI-MKS 8 Speed of light...

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