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