Outer: Construct matrix from lists

In Mathematica, a quick way to construct a matrix from lists is through Outer. Let us consider two lists defined as

a={a1,a2,a3};
b={b1,b2};

Then the following command

Outer[f, a, b]

gives a matrix of the form

f[a1,b1] f[a1,b2]
f[a2,b1] f[a2,b2]
f[a3,b1] f[a3,b2]

A practical example is given below. Consider d-band electrons with spins. There are five d-orbitals and two spin states. Suppose orbital and spin stores the orbital and spin part of the state vector. The complete basis can be obtained by

Flatten[Outer[Join, orbital, spin, 1], 1]