By P. W. Anderson

ISBN-10: 9812388656

ISBN-13: 9789812388650

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**Extra resources for A Career In Theoretical Physics**

**Example text**

Then it is easy to show that (47) is the same as (j/ljim\jflfiM) r= f »^n 2-wbdb £ M, m, i M,m,m' (2ji+l) XlSmm^^-(m\T^(b)\m')(ix'\Tf(b)\ixU. (jAjtm'\j/ln'M) (47') A similar formula can be written in the two molecule case of Eq. (46). BROADENING tions with the assumption that J'Hi'dt/h use the following procedure: T=T0+T1+T2+---, is small. We 7-0=1, r' #i'(0 ihTi = HiT„; 7\(0= df, J^„ ihf^H/Tu (49) ih ' Hi(t') T2(t) = •J-^ ih r"Hi'(t") ih df J ', etc. If we could assume that 777(0 commuted with Hi'(t") at all times, the result of this process would be simply the scalar solution of the linear differential Eq.

1. 3. SVJmiddie: 1 2jd-l m, m', M r L i a= f 2irbdbS{b), (JAj m I JAliM) (jAjiM\ (m\I (mlP^m) —r Referring to the definition (51) of P, it appears that this, the first "shift" term in a, is just the first term in the simple phase-shift approach, averaged over all directions. There are two possibilities for obtaining second-order terms in the S sum. We have the choice of taking To(XT/ or vice versa, or of taking the terms involving 7VX7Y. The former pair of terms follow precisely as did the Si terms; we call these (S2) outer.

If we could assume that 777(0 commuted with Hi'(t") at all times, the result of this process would be simply the scalar solution of the linear differential Eq. (9'): T(t) (50) On the other hand, it is clear from the definition (10) of Hi that it does not commute with itself at all times, but only because 77i and H0 do not commute. Hi(t) is a function of the coordinates only, in general, and will always commute with itself. An investigation was made into the size and meaning of the "non^commuting" terms by which (50) differs from the accurate solution of (49).

### A Career In Theoretical Physics by P. W. Anderson

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