Eigenfunction g

As an example of another property, consider momentum. The eigenfunctions g of pji are found by solving... 

The properties (7.88) of the Dirac delta function agree with the properties (7.78) and (7.79) of the position eigenfunctions g (jr). We therefore tentatively set... 

Postulate 4. If B is any linear Hermitian operator that represents a physically observable property, then the eigenfunctions g, of B form a complete set. 

First, we show that if there exists a common complete set of eigenfnnctions for two linear operators then these operators commute. Let A and B denote two linear operators that have a conunon complete set of eigenfunctions g, g2, ... 

As with any quantum-mechanical operator, we are interested in the eigenvalues c, and the eigenfunctions g, of the parity operator ... 

Suppose Ag = a . Let the eigenfunctions g be expanded in terms of the complete orthonormal set fi) according to Substitute this expansion into = a , multiply by/ integrate over all space, and show that the set of equations — a Sii )c = 0... 

---