Abstract
It is always possible to represent a linear operator L as a matrix. The representation of the linear operator L on the basis represented by a complete set of eigenfunctions {u n(r)} is given by the matrix constituted by the following matrix elements:
. (A.1) If L = L°, then L *mn = L mn. In detail,
. (A.2) If {u n(r)} is an orthonormal set of eigenfunctions of the Hilbert space, then (u n, u m) =δnm. (A.3) If {u n(r)} is a set of orthonormal eigenfunctions of the operator L, then the representation of L on the basis {u n(r)} is a diagonal matrix. This can be written as Lu n = λn u n, (A.4) and, as a consequence,
. (A.5)
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© 2003 Springer-Verlag Berlin Heidelberg
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(2003). Matrices and Operators. In: Dapor, M. (eds) Electron-Beam Interactions with Solids. Springer Tracts in Modern Physics, vol 186. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36507-9_7
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DOI: https://doi.org/10.1007/3-540-36507-9_7
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