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Exploring Wave-Particle Duality: de Broglie's Hypothesis & Uncertainty Principle - Prof. T, Study notes of Physics

The concept of wave properties in particles, as proposed by louis de broglie. How matter, like light, can exhibit both particle and wave behavior. It also introduces the uncertainty principle and its implications for measuring the position and momentum of subatomic particles. Examples and problems related to these concepts.

Typology: Study notes

Pre 2010

Uploaded on 08/18/2009

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40.5TheWavePropertiesofParticles
(1923)LouisdeBroglie
Q.Iflightcanactlikeaparticle&awave,canmatter(made
upofparticles)actlikeawave?
A. Yes .
Ifaparticlehaswaveproperties,itsmomentumwillhavea
momentumlikethatofaphoton:
andtheenergywouldbegivenbythesameexpressionas
foraphoton:
Themostcommonwaywaveeffectsareseenin
matterisviadiffractionthroughcrystals.
Title:Apr298:03AM(1of9)
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40.5 The Wave Properties of Particles

(1923) Louis deBroglie

Q. If light can act like a particle & a wave, can matter (made

up of particles) act like a wave?

A. Yes.

If a particle has wave properties, its momentum will have a

momentum like that of a photon:

and the energy would be given by the same expression as

for a photon:

The most common way wave effects are seen in

matter is via diffraction through crystals.

What's my wavelength as I walk at 2.2 m/s (my mass is 75

kg).

What's the wavelength of an electron that's been accelerated

through a 3.0volt potential (giving it a speed of

Example: You measure the position of a dynamics cart

(mass = 0.495 kg) using a scale marked off in mm. What's

the best precision you could obtain in measuring its velocity?

To be specific, lets suppose Δx = 0.3 mm

But for an electron in a H atom, using the idea of an electron

cloud, all we can say is that the electron is "somewhere" in

the atom, so Δx is the size of a H atom.

Chapter 41

41.4 The Schrodinger Equation

Since matter has wave properties, it can be described by

a wave equation. But what is "waving?"

We describe a particle with a probability distribution,

Ψ(x) ("psi") with wave equation:

(probability

that it's

somewhere

is 100%)

Ψ² is the probability of finding the particle at a particular

place

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