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Example text

We may define the using ket 1n) and bra < n I. Its x-representation is

E is the eigenvalue, the size of the system being V / A3, or V/ A3 = V + dV (d V = - 38 V) . Since the real Hamiltonian of the system is not changed, we let the term in the curly brackets { } in the above equation be eliminated by adding a term of the same as { } but with the opposite sign; the change in the eigenvalue is then dE = - 8 N*(AX) = -8 N*(x) au} au} jY { 2. ax 2 + L x~ t/J(Jex)dxIN*(Ax)t/J(Ax)dx 02 { L ax 2 + 2. x~ t/J(x)dxIN*(x)t/J(x)dx to first order in 8. 14] dE 2 {/ - dV=3V \ 02 1 au )} 1 -22.

9) for the density matrix can be transformed into an equation of motion for Wigner's distribution function. Let p2 £(p, x) = 2m + U(x) be the Hamiltonian, then the equation of motion for a density matrix

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