FinalExample2

FinalExample2 - FINAL EXAMPLE 2 SI-MKS Speed of light in...

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Applied quantum mechanics FINAL EXAMPLE 2 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 The time-independent Schrödinger equation for Hamiltonian has known orthonormal eigen- functions such that where . In the presence of a time-dependent change in potential applied at time t > 0 the system evolves in time according to where and are time-dependent coefficients. (a) Show that for time t > 0 where and . (30%) (b) In first-order time-dependent perturbation theory is assumed small and is approximated by its initial value . Show that for time t
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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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FinalExample2 - FINAL EXAMPLE 2 SI-MKS Speed of light in...

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