Relativistic De Broglie Relation

In summary, the conversation is about deriving the De Broglie relation for a relativistic particle in terms of kinetic energy. The desired equation is lambda = (hc)/sqrt(K(K+2mc^2)), which can be derived from the expressions pc = sqrt(K^2 + 2Kmc^2) and E^2 = (pc)^2 + (mc^2)^2. The person is having trouble manipulating the expressions to get the exact equation.
  • #1
CoreyJKelly
12
0
so I'm trying to derive the De Broglie relation:

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

for a relativistic particle.. I know that it can be simply written in terms of the relativistic momentum, but to complicate matters, I'm asked to write it in terms of the Kinetic energy.. the expression I'm looking for is:

[tex]\lambda[/tex] = [tex]\frac{h c}{\sqrt{K(K + 2mc^{2})}}[/tex]

I'm getting really close.. but no matter how i manipulate the expressions, i can't seem to get this exact equation... any ideas?
 
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  • #2
well

[tex] pc = \sqrt{K^2 + 2Kmc^2} [/tex]

which is derived from:

[tex] E = K + mc^2 [/tex]

And:

[tex] E^2 = (pc)^2 + (mc^2)^2 [/tex]
 
  • #3
haha, i figured it'd be something simple... thanks!
 

1. What is the Relativistic De Broglie Relation?

The Relativistic De Broglie Relation is a fundamental principle in quantum mechanics that describes the relationship between the momentum and wavelength of a particle. It states that the momentum of a particle is equal to its mass multiplied by its velocity, and that the wavelength of the particle is inversely proportional to its momentum.

2. Who discovered the Relativistic De Broglie Relation?

The Relativistic De Broglie Relation was first proposed by French physicist Louis de Broglie in 1924. He was inspired by the wave-particle duality of light, which suggests that particles can have both wave-like and particle-like properties.

3. How does the Relativistic De Broglie Relation differ from the classical De Broglie Relation?

The classical De Broglie Relation only applies to non-relativistic particles with speeds much lower than the speed of light. The Relativistic De Broglie Relation, on the other hand, takes into account the effects of special relativity and applies to all particles, including those with high speeds.

4. What are the implications of the Relativistic De Broglie Relation?

The Relativistic De Broglie Relation has significant implications for our understanding of the behavior of particles at the quantum level. It helps explain phenomena such as particle-wave duality and the uncertainty principle, and is a crucial component of the Schrödinger equation, which describes the behavior of quantum systems.

5. How is the Relativistic De Broglie Relation used in practical applications?

The Relativistic De Broglie Relation is used in various fields, such as particle physics, quantum mechanics, and material science. It is also used in technologies such as electron microscopes and particle accelerators, which rely on the wave-like behavior of particles to function. Additionally, the equation has been instrumental in the development of quantum computing and other quantum technologies.

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