Differentiate De Broglies Theorem

In summary, De Broglie's Theorem is a fundamental principle in quantum mechanics that states that all particles have wave-like and particle-like properties. It was first proposed by French physicist Louis de Broglie in 1924 and is unique in its application to both matter particles and electromagnetic waves. The mathematical equation for De Broglie's Theorem is λ = h/mv, and it is used in various fields to understand the behavior of particles at the atomic and subatomic level. It has also been applied in the development of technologies such as electron microscopes and particle accelerators.
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Homework Statement



Someone has written down in some notes about differentiating DeBroglies Theorem.

They've started with Px =h/λ
(That's P sub x)

Then they've simply said, this differentiated is:

ΔPx = [-h/(λ^2)]Δλ

How have they done this? What method? What have they differentiated with respect to?

Thank you!

Homework Equations





The Attempt at a Solution

 
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respect to λ

P = h/λ

dP/dλ = (-1/λ^2) * h

dP = -(h/λ^2)dλ
 

FAQ: Differentiate De Broglies Theorem

What is De Broglie's Theorem?

De Broglie's Theorem is a fundamental principle in quantum mechanics that states that all particles, including matter, have both wave-like and particle-like properties.

Who proposed De Broglie's Theorem?

De Broglie's Theorem was first proposed by French physicist Louis de Broglie in 1924 as a solution to the wave-particle duality paradox.

How is De Broglie's Theorem different from other quantum theories?

De Broglie's Theorem is unique in that it applies to both matter particles (such as electrons) and electromagnetic waves, while other quantum theories only apply to one or the other.

What is the mathematical equation for De Broglie's Theorem?

The equation for De Broglie's Theorem is λ = h/mv, where λ is the wavelength of the particle, h is Planck's constant, m is the mass of the particle, and v is its velocity.

How is De Broglie's Theorem applied in real-world situations?

De Broglie's Theorem is used in various fields such as quantum mechanics, particle physics, and chemistry to understand the behavior of particles at the atomic and subatomic level. It has also been applied in the development of technologies such as electron microscopes and particle accelerators.

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