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8.1.4 Eigenvalues of Hermitean operators

Eigenvalues and eigen vectors of Hermitean operators are defined as for matrices, i.e., where there is a matrix-vector product we get an operator acting on a function, and the eigenvalue/function equation becomes

$\displaystyle \hat{O}$f (x) = onf (x), (8.5)

where on is a number (the ``eigenvalue'' )and f (x) is the ``eigenfunction''.

A list of important properties of the eigenvalue-eigenfunction pairs for Hermitean operators are:

1.
The eigenvalues of an Hermitean operator are all real.
2.
The eigenfunctions for different eigenvalues are orthogonal.
3.
The set of all eigenfunction is complete.


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Next: 8.1.5 Outcome of a Up: 8.1 Key postulates Previous: 8.1.3 Hermitean operators

© 1998 Niels Walet, UMIST
Email Niels.Walet@umist.ac.uk