The Determination of the Scattering Potential From the Spectral Measure Function

Cover The Determination of the Scattering Potential From the Spectral Measure Function
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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