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?