De Broglie Wavelength Derivation

In summary, the conversation discusses the relationship between kinetic energy and momentum in Classical Mechanics. It is stated that the derivative of kinetic energy with respect to velocity is momentum. The conversation also mentions the use of the variables lambda and h (Planck's Constant) in the equation E=hf. It is then suggested that this equation can be rearranged to show that the de Broglie wavelength is equal to Planck's Constant divided by momentum. However, it is noted that this is a postulate and not a rigorous derivation.
  • #1
Goalie33
33
0
In Classical Mechanics the derivative of Kinetic energy with respect to velocity is momentum, so I was wondering if this is valid:

In this L is lambda or wavelength and h is Planck's Constant.

E=hf, therefore E=h(v/L)
This means that dE/dv=h/L.(h and L are constants and the derivative of v would be 1.)
Rearranging this we get:
L=h/p.

I just wanted to know if this is considered valid.
 
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  • #2
in E=hf, 'v' is equal to c, which is a constant!

One does not 'derive' de Broglie Wavelength, one postulates it.

E = hc/L, E/c = h/L

But E/c is the momentum of a massless particle, e.g. the photon. Hence, we postulate that this result can be more general to be valid for massive particles with momentum p.

p = h/L

So it is not a rigour derivation, but a bold postulate, which turned out to work fine :-)
 

1. What is the De Broglie Wavelength Derivation?

The De Broglie Wavelength Derivation is a mathematical derivation that explains the relationship between the momentum and wavelength of a particle, proposed by French physicist Louis de Broglie in 1924. It is based on the concept of wave-particle duality, which states that particles can exhibit both wave-like and particle-like behavior.

2. How is the De Broglie Wavelength Derivation derived?

The De Broglie Wavelength Derivation is derived using the principles of quantum mechanics, specifically the Schrödinger equation and Planck's constant. It involves calculating the wavelength of a particle by dividing Planck's constant by the momentum of the particle.

3. What is the significance of the De Broglie Wavelength Derivation?

The De Broglie Wavelength Derivation is significant because it provides a mathematical explanation for the wave-like behavior of particles, which was previously only understood through experimental evidence. It also helped pave the way for the development of quantum mechanics and our understanding of the behavior of subatomic particles.

4. Can the De Broglie Wavelength Derivation be applied to all particles?

Yes, the De Broglie Wavelength Derivation can be applied to all particles, including electrons, protons, and even larger particles such as atoms. However, it is most commonly used for particles with small masses, such as electrons, due to the high values of Planck's constant for larger particles.

5. How does the De Broglie Wavelength Derivation relate to the Uncertainty Principle?

The De Broglie Wavelength Derivation is related to the Uncertainty Principle, which states that the more precisely we know the momentum of a particle, the less precisely we know its position, and vice versa. This is because the De Broglie Wavelength represents the uncertainty in the position of a particle due to its wave-like behavior.

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