Relationship between the momentum and position of particles in the double slit experiment

  • #1
Ad VanderVen
156
10
TL;DR Summary
In the double-slit experiment with two open slits, is there a fixed relationship between the momentum (p) of the particle immediately after passing through the slit and the position (q) of the impact on the screen?
In the double-slit experiment with two open slits, is there a fixed relationship between the momentum (p) of the particle immediately after passing through the slit and the position (q) of the impact on the screen?
 

Answers and Replies

  • #2
hutchphd
Science Advisor
Homework Helper
2022 Award
5,363
4,529
Yes. The relationship is called Schrodinger's Equation for a non-relativistc massive particle.
If you wish a more specific answer you will need to formulate a more specific question.
 
  • #3
Ad VanderVen
156
10
My specific question is, that I have a formula for the probability density function of the momentum (p) of the particle immediately after it passes through the slit in the double-slit experiment with two open slits and I want to derive from that formula a formula for the probability density function of the position (q) of the impact on the screen?
 
  • #4
hutchphd
Science Advisor
Homework Helper
2022 Award
5,363
4,529
Then you need to solve Schrodinger to match your specific boundary conditions in time and space. This will likely be very difficult.
There are many approximation techniques that are useful for particular situations. What does your formula look like?
 
  • #5
Ad VanderVen
156
10
It is formula (11) from Uffink and Hilgevoord. (1985):

$$\begin{align}
\phi \left(p \right) \, = \, \frac{\sqrt{2}~\sqrt{\frac{a }{\pi }}~\cos \left(A ~p \right)~\sin \left(a ~p \right)}{a ~p }
\end{align}$$

Reference

Uffink, J.B.M. and Hilgevoord, J. (1985). Uncertainty Principle and Uncertainty Relations. Foundations of Physics, Vol. 15, No. 9,
 
Last edited:

Suggested for: Relationship between the momentum and position of particles in the double slit experiment

Replies
7
Views
555
  • Last Post
Replies
3
Views
379
  • Last Post
Replies
4
Views
456
Replies
16
Views
512
Replies
8
Views
459
Replies
0
Views
392
Replies
19
Views
871
Replies
26
Views
554
  • Last Post
Replies
5
Views
461
Top