Measuring the Electron's Momentum Through a Slot

[renegade05]

Homework Statement

Consider an electron incident on a screen with a narrow slot of width 2d. Assume
that the electron is moving with velocity v in the direction perpendicular to the screen and
that its wavefunction is uniformly spread over the slit and its vicinity, as shown. After going
through the slit, the electron hits a detector screen a distance D away. Assume that d << D.

(a)We can think of this set up as a way to measure the momentum of the electron after
it passed through the slit. If the electron hits the detector screen at a point x away from the
point directly ligned up with the center of the slit (see Figure), what was the x-component
of its momentum just after it passed through the slit?

Homework Equations

p = mv

The Attempt at a Solution

Am I wrong to assume this is just equal to (m of electron)*sin(y)=momentum in x direction ?

I feel like this is too easy.

 

[Simon Bridge]

See:
http://arxiv.org/pdf/quant-ph/0703126]