Theoretical Physics 6 by Wolfgang Nolting

Author:Wolfgang Nolting
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

(3.122)

One easily realizes that rows and columns of a unitary matrix are orthonormalized:

(3.123)

If one chooses as the basis of just the complete set | a n 〉 of eigen-states of the Hermitian operator A, then the matrix A has a diagonal form, where on the main diagonal just the eigen-values a n of A appear:

(3.124)

It is important in this connection that there always exists a unitary transformation which brings a matrix A into the diagonal form (3.124). That can be seen as follows:

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