Upper Bounds On Scattering Lengths When Composite Bound States Exist

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Upper Bounds On Scattering Lengths When Composite Bound States Exist
Tony Randall
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Is a sufficiently accurate ground state trial function so that /_ -j H ll = E l K ° # (If this last inequality is not satisfied, the method described below will not be applicable. This, however, does not represent a serious limitation since a trial function with the required accuracy can almost always be found. ) (2) (2) It then follows that the eigenvalues of the above matrix, E^ and E^, satisfy the relations from Theorem 1, and 4 2) >o, Ee 2 Jw(X)/w(X)dr 2 « ( 2 - 9 > We have then succeeded... in our purpose in that we have obtained a bound which does not require a knowledge of the exact bound state function nor of its energy, and which has at the same time avoided the use of the rigorous but often very crude Schwarz inequality.

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