The Determination of the Scattering Potential From the Spectral Measure Function

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The Determination of the Scattering Potential From the Spectral Measure Function
Irvin W Kay
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- 12 - For each value of a and E. The operator maps an 'eigenvector' of the extended operator H into an eigenvector H with the same value of a as a degeneracy- label.
Generally the eigenfunctions of H corresponding to the discrete spectrum satisfy the following orthogonality relation: (3. 20) - 6(i, j) , where 5(i, j) is the Kronecker 5. The matrix is a positive definite Hermitian matrix in the space of eigenfunctions of the operator A corresponding to a fixed eigenvalue E. Of H. In the case
...where the eigenfunctions belonging to the same eigenvalue E but having different degeneracy labels have been made orthogonal to each other, woiald have the form = C^g6(a, b), The constant C. (which is always positive) is the normalization constant for the ia eigenfunction lH, A}E. , a >, that is, - C^^^ .
The operator has a positive-definite inverse which we denote by

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