DIRAC NOTATION

Notations• Bra and Ket•Inner products and Projection operators

ExamplesEigenvalues and EigenvectorsPostulates of QM

Dirac Notations

Dirac Notations

Dirac Notations

More general superposition

• The index of bases is a continuous variable x:

• A State in terms of wavefunction

= ( )dx x x

Inner product

Orthogonal and normalized bases

• Used implicitly

For continuous variables

iji j

( )x x x x

Projection operators

Complete space

ˆdx x x IThe complete space may contain two parts, one with discrete index and one with continuous variable!

Projection operators

Eigenvalue and eigenvectors

Postulations of QM

Postulations of QM