De Broglie wavelength and velocity

  • Thread starter durant35
  • Start date
  • #1
293
11
I was wondering about the equation for the de Broglie wavelength which indicates that the wavelength of any object is shorter when the object is moving faster. Why does this occur? And how we connect this with special relativity where the velocity depends on the frame of reference.
 

Answers and Replies

  • #2
Vanadium 50
Staff Emeritus
Science Advisor
Education Advisor
2019 Award
25,640
8,828
The wavelength is shorter because the momentum is higher. De Broglie was developed before SR, so it is not a relativistic theory.
 
  • Like
Likes bhobba
  • #3
jtbell
Mentor
15,659
3,729
And how we connect this with special relativity where the velocity depends on the frame of reference.
The wavelength also depends on the frame of reference. Note that velocity and wavelength depend on the frame of reference, even in non-relativistic mechanics.
 
Last edited:
  • #4
Vanadium 50
Staff Emeritus
Science Advisor
Education Advisor
2019 Award
25,640
8,828
Doc Al pointed out that I was wrong about the sequence of events - DeBroglie was after SR. However, it is still a non-relativistic theory.
 
  • #5
DrClaude
Mentor
7,497
3,773
Doc Al pointed out that I was wrong about the sequence of events - DeBroglie was after SR. However, it is still a non-relativistic theory.
I'm sorry, but de Broglie's thesis from 1924 starts from ##E = mc^2##. It is then by combining this with Planck's ##E = h \nu## that he ends up with a wavelength for a matter wave. I don't see how this is not a relativistic theory.

A reproduction of the thesis (in French) can be found at https://tel.archives-ouvertes.fr/tel-00006807/en/
 
  • #6
159
55
  • #8
159
55
That link doesn't work.
Hm. Works here. What kind of error do you get?
 
  • #9
Vanadium 50
Staff Emeritus
Science Advisor
Education Advisor
2019 Award
25,640
8,828
DeBroglie essentially takes a fundamentally NR equation and stick in the relativistic expression for momentum in it. That doesn't make it a relativistic equation. (If it did, GR would have been invented a decade earlier.) As pointed out earlier, it doesn't transform right. In modern language, it takes one component of a 4-vector and relates it to three components of a different 4-vector.
 
  • #10
DrClaude
Mentor
7,497
3,773
Hm. Works here. What kind of error do you get?
Server not found.
 

Related Threads on De Broglie wavelength and velocity

  • Last Post
Replies
15
Views
12K
  • Last Post
Replies
2
Views
4K
  • Last Post
Replies
1
Views
3K
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
9
Views
6K
  • Last Post
Replies
4
Views
4K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
3
Views
2K
Replies
10
Views
1K
Top