Bounds On Elements of the S Matrix for Elastic Scattering One Dimensional Scatt
Bounds On Elements of the S Matrix for Elastic Scattering One Dimensional Scatt
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*A, phase shift 5 . {\i) corresponding to the comparison potential is obtained when X = 1, and 5. (^) when X = 0. It follows from Eq. (39) that 5 . (^) is an upper bound on 6. (n), 8^i(n) ^ 6. (^). (ho).
As before, we are required to keep track of the eigenphases as X is varied continuously from zero to one. The only difficulty occurs at a possible crossing point, but B. (|a, X) = 5. (|a, X) already implies that these eigen- 19 phase shifts axe greater than the true values and they can only inc...rease as X approaches one. Eq. (^O) is therefore valid in any case.
By introducing another comparison potential such that A V is non- negative^ it can be shown in a similar fashion that the corresponding eigenphase shifts 6 (|a) are lower boimds on the 5. ((i)^ B^. (u) § 5. (^) . (J+1) The way in which the bounding curves obtained from the comparison potentials can be used to calculate lower bounds a and p on a and on p, respectively, is illustrated for a typical case in Figure 2. It y is clear from Figure 2 that if the comparison potentials do not approxi- mate the actual potential fairly closely, it may not be possible to ob- tain lower bounds on a and on p .
What to read after Bounds On Elements of the S Matrix for Elastic Scattering One Dimensional Scatt?
You can find similar books in the "Read Also" column, or choose other free books by Ralph Bartram to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
*A, phase shift 5 . {\i) corresponding to the comparison potential is obtained when X = 1, and 5. (^) when X = 0. It follows from Eq. (39) that 5 . (^) is an upper bound on 6. (n), 8^i(n) ^ 6. (^). (ho).
As before, we are required to keep track of the eigenphases as X is varied continuously from zero to one. The only difficulty occurs at a possible crossing point, but B. (|a, X) = 5. (|a, X) already implies that these eigen- 19 phase shifts axe greater than the true values and they can only inc...rease as X approaches one. Eq. (^O) is therefore valid in any case.
By introducing another comparison potential such that A V is non- negative^ it can be shown in a similar fashion that the corresponding eigenphase shifts 6 (|a) are lower boimds on the 5. ((i)^ B^. (u) § 5. (^) . (J+1) The way in which the bounding curves obtained from the comparison potentials can be used to calculate lower bounds a and p on a and on p, respectively, is illustrated for a typical case in Figure 2. It y is clear from Figure 2 that if the comparison potentials do not approxi- mate the actual potential fairly closely, it may not be possible to ob- tain lower bounds on a and on p .
What to read after Bounds On Elements of the S Matrix for Elastic Scattering One Dimensional Scatt?
You can find similar books in the "Read Also" column, or choose other free books by Ralph Bartram to read onlineMoreLess
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