Unitary transformation

A unitary transformation of a set of vectors to another set of vectors preserves the lengths of the vectors and the angles between the vectors.

In other words, a unitary transformation is a rotation of axes in the Hilbert space. This implies that if the transformation involves matrices of eigenvectors, the eigenvalues of the eigenvectors are preserved. Consider 2 complete sets of orthonormal bases:

where is the identity matrix.

The relation between the two basis sets are

where are elements of the transformation matrix U.

We say that is transformed to by . Similarly, we have .

The reverse transformation of eq68 is:


Show that .





Next article: Slater determinant of unitarily transformed spin orbitals
Previous article: Slater determinant
Content page of computational chemistry
Content page of advanced chemistry
Main content page

Leave a Reply

Your email address will not be published. Required fields are marked *