De Broglie Waves: Frequency, Wavelength & Momentum

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Discussion Overview

The discussion revolves around De Broglie waves, focusing on their properties such as frequency, wavelength, and momentum. Participants explore the implications of the De Broglie wavelength formula and its interpretations, as well as related concepts such as wave interference and particle interactions.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • One participant states that De Broglie waves are equivalent to Planck's constant divided by the particle's momentum, questioning the relationship to frequency and wavelength.
  • Another participant confirms the formula for wavelength as λ = h/p and clarifies that these waves are abstract, representing probabilities rather than physical waves like those on water.
  • Some participants express interest in the largest observable matter waves and speculate on their characteristics.
  • Questions arise regarding the effects of destructive interference between wave particles, with one participant suggesting that the probability of finding the particles would be zero.
  • Another participant discusses particle annihilation, specifically mentioning electron-positron interactions and the conversion of energy into other particles, while referencing conservation laws.
  • Several posts diverge into a historical discussion about tensor calculus and its relation to figures like Gauss and Riemann, which some participants feel detracts from the original topic.

Areas of Agreement / Disagreement

Participants exhibit a mix of agreement and disagreement, particularly regarding the interpretations of De Broglie waves and the implications of wave interference. The historical discussion on mathematics also shows differing perspectives, indicating unresolved views on the topic.

Contextual Notes

The discussion includes various assumptions about the nature of waves and particles, the definitions of terms like wavelength and momentum, and the implications of conservation laws, which are not fully resolved.

Who May Find This Useful

This discussion may be of interest to those studying quantum mechanics, wave-particle duality, and the historical context of mathematical concepts in physics.

DB
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Correct me where I'm wrong. De Broglie waves, are extremely small waves of matter equivilant to Planck's constant over the the particles momentum??

[tex]\frac{h}{p}[/tex]

If so these would be extremely small waves. But if the formula is right, what exactly is the formula porportional too? Frequency, wavelength?

Thanks
 
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The formula is

[tex]\lambda = \frac{h}{p}[/tex]

where lambda is the wavelength of the wave. I think that was your question.

I would also like to point out, in case you did not know, that these "waves of matter" are not waves like those you see on the sea happening on the surface of matter. They are "abstract waves" whose nature were unknown at the time of their discovery by De Broglie. It was later found that the waves reprent the probability of finding the particle at a certain position in space: the higher the amplitude of the wave at that point, the higher the probability.

Another remark: the wavelength is not necessarily small. As soon has you have a momentum that is about as small as h, then the wavelength is big enough that you could see the waves if they were visible. For exemple, if p=h, the wavelength is of 1 meter!
 
Thanks quasar, that's what I was looking for, the formula is equivalent to the wavelength. And I guess I never thought that the smaller the momentum the bigger the wavelength, interesting stuff.
 
What is the largest matter wave that a person has observered? What would it look like? I mean in something very large with a large wave... Thanks
 
derekmohammed said:
What is the largest matter wave that a person has observed? What would it look like? I mean in something very large with a large wave... Thanks

How about a low E neutrino at one of the South Pole detectors?
 
destructive interference

What happens if you have two similar wave particles interfere destructively: would the particles disappear? probably not... but what happens?
 
jet10 said:
What happens if you have two similar wave particles interfere destructively: would the particles disappear? probably not... but what happens?

The probabity of finding the particles there would be zero.
 
where does the energy or the particle go to, if the two waves completely eliminate each other?
 
jet10 said:
where does the energy or the particle go to, if the two waves completely eliminate each other?


For example if an electron and a positron interact they will annihilate each other. This means that the energy coming from these two particles is converted into other particles like a photon pair for example. Basically what will happen is conversion into other particles. The rules that need to be respected are called conservation laws. for example an electron and a positron have opposite charge. This implies that the resulting photons may not exhibit charge due to this conservationlaw. Ofcourse photons DO NOT have charge so tha's ok. Also energy needs to be conserved,...

regards
marlon
 
  • #10
marlon said:
For example if an electron and a positron interact they will annihilate each other. This means that the energy coming from these two particles is converted into other particles like a photon pair for example. Basically what will happen is conversion into other particles. The rules that need to be respected are called conservation laws. for example an electron and a positron have opposite charge. This implies that the resulting photons may not exhibit charge due to this conservationlaw. Ofcourse photons DO NOT have charge so tha's ok. Also energy needs to be conserved,...

regards
marlon

...4-momentum actually.Lepton number,spin,isospin,baryon number,etc...

Daniel.

PS.U know that Gauss and Riemann had nothing to do with absolute differential calculus... :wink: So let's not put them together with Ricci and Christoffel vs.quaternions of Mr.Hamilton. :wink:
 
  • #11
dextercioby said:
PS.U know that Gauss and Riemann had nothing to do with absolute differential calculus... :wink: So let's not put them together with Ricci and Christoffel vs.quaternions of Mr.Hamilton. :wink:


i hope this is meant to be a joke...

marlon
 
  • #12
Nope,tensor calculus was developed after the works of Gauss and Riemann. :approve: You may remember who put the names "tensor" into physics... :wink: What about "curl"??What about "gradien"??""Nabla"??"Divergence"??"Covariant differential"?Christoffel symbols??(Nope,that's too simple... :-p )

History,Marlon...

Daniel.
 
  • #13
dextercioby said:
Nope,tensor calculus was developed after the works of Gauss and Riemann.

Indeed, there's your answer : PIONEERS dexter

History,Marlon...

Daniel.

It sure is, dexter...

marlon
 
  • #14
marlon said:
Indeed, there's your answer : PIONEERS dexter
marlon

Nope,pioneer was Augustin Cauchy.He used the notion "tensor" when speaking about TENSIONS (quite similar to "tensor",right ?? :wink: ) in fluids.

Tensor calculus means calculus with tensors...And it doesn't concern K.F. Gauss and B.Riemann.

BTW,they pioneered differential geometry.Tensor calculus was merged with differential geometry in the 1900-s by Weyl and Elie Cartan... :wink:

Daniel.

EDIT:Maybe we should allow a mathematician have his say... :wink:

EDIT2:Anyway,we've diverted this thread from de Broglie's waves to history of mathematics... :-p
 
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