Quantum Statistics And the Boltzmann Equation
Quantum Statistics And the Boltzmann Equation
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k. The functional differential equation The work in this section parallels the development of the classical case given in Sections 2 and 3 of [l] . In fact, if we simply replace the classical density function D of [l] by the Wigner function w^, and the operation j ({)( | q . -q, | ) J \ hy - G •, the analysis becomes identical. Hence we shall only outline the development here, and refer to [l] for the details .
We begin by introducing the functional n Ljt, u] =jr, jt, x_, ... , xj n_^ [l + w(x.... )]dx^... Dx^, (^. 1) which is defined on the domain of functions u(x) for which the integral converges . By functional differentiation we obtain 6u(x^)... Su(Xg) U;=0 n (n-s) E" (t, x, ... , x ); s = 0, 1. 2, . .. , n. {h. 2) n, s^ ^ 1^ ' s" With the aid of (^^-. 2), L may now be expressed as a (finite) series expan- sion around u = 0.
[t, u] =1+ S Tr(l-^)---(l -^) 21 Ix /. S-1, / \, it, ^^>. -. , ^^M.^).. M^^H^^...^^. (^. 5) A differential equation for L may be obtained by multiplying (3-9) n by IT [l + vu(x.
What to read after Quantum Statistics And the Boltzmann Equation?
You can find similar books in the "Read Also" column, or choose other free books by Robert M Lewis to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
k. The functional differential equation The work in this section parallels the development of the classical case given in Sections 2 and 3 of [l] . In fact, if we simply replace the classical density function D of [l] by the Wigner function w^, and the operation j ({)( | q . -q, | ) J \ hy - G •, the analysis becomes identical. Hence we shall only outline the development here, and refer to [l] for the details .
We begin by introducing the functional n Ljt, u] =jr, jt, x_, ... , xj n_^ [l + w(x.... )]dx^... Dx^, (^. 1) which is defined on the domain of functions u(x) for which the integral converges . By functional differentiation we obtain 6u(x^)... Su(Xg) U;=0 n (n-s) E" (t, x, ... , x ); s = 0, 1. 2, . .. , n. {h. 2) n, s^ ^ 1^ ' s" With the aid of (^^-. 2), L may now be expressed as a (finite) series expan- sion around u = 0.
[t, u] =1+ S Tr(l-^)---(l -^) 21 Ix /. S-1, / \, it, ^^>. -. , ^^M.^).. M^^H^^...^^. (^. 5) A differential equation for L may be obtained by multiplying (3-9) n by IT [l + vu(x.
What to read after Quantum Statistics And the Boltzmann Equation?
You can find similar books in the "Read Also" column, or choose other free books by Robert M Lewis to read onlineMoreLess
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