FinalExample3

FinalExample3 - FINAL EXAMPLE 3 SI-MKS Speed of light in...

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Applied quantum mechanics FINAL EXAMPLE 3 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 6.58211889 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 In first-order time-dependent perturbation theory a particle initially in eigenstate of the unper- turbed Hamiltonian scatters into state with probability after the perturbation is applied at time . (a) Derive the expression for the time dependent coefficient where the matrix element and is the difference in eigenen- ergies of the states and . (40%) (b) An electron is initially in the ground state of a one dimensional harmonic oscillator with Hamiltonian where
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FinalExample3 - FINAL EXAMPLE 3 SI-MKS Speed of light in...

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