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( a) The Hamiltonian is diagonal in the position; the first and last terms are the energies of the electrons and phonons respectively. ( a) Some boys are sharp and intelligent.

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The other terms is the only interaction, the electron- phonon coupling that dresses up the electrons. 1 ( disappearing source provision), the $ 190, 000 balance will be deemed to be used to produce income.

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If a( x), b( x) and c( x) are continuous with a( x) never zero, then the ODE a( x) y/ / + b( x) y/ + c( x) y = 0 has a unique solution y( x) with given values for y( x0) and y/ ( x0).