5.4.2 The linear momentum eigenfunction

1
What is the one-dimensional linear momentum eigenfunction?
2
Sketch its real part, its imaginary part, and its square magnitude.
3
What is the three-dimensional linear momentum eigenfunction?
4
What is the coefficient $\Phi$ of the eigenfunction called?
5
Normally, the square magnitude of the coefficient should give the probability of measuring the corresponding linear momentum. Why is this untrue for position eigenfunctions?
6
So what does the square magnitude of the coefficient give?
7
Write the wave function $\Psi$ out fully in terms of the linear momentum eigenfunctions and their coefficients.
8
What is the above transformation of $\Phi$ into $\Psi$ called?