Lecture 22 Quantum Physics II

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Lecture 22Quantum Physics II
Chapter 27.6 ? 27.9
Outline

• De Broglie Wavelength
• The Electron Microscope
• The Wave Function and The Uncertainty Principle

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Matter Waves
In 1924 Louis de Broglie suggested that moving
objects in some respects act like waves.
A particle of mass m and speed v behaves like a
wave with wavelength ?, so that
h
Planks constant ? ?? de Broglie
wavelength ?????? mv
momentum
Later it was shown that electrons exhibit both
diffraction and interference, and their
wavelengths are in agreement with the de Broglie
wavelength.
Application the electron microscope
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Wave Function
In water waves, the height of the water surface
varies. In sound waves, it is the air
pressure. In electromagnetic waves, it is
electric and magnetic fields.
In matter waves, the wave function ? (psi)
varies. ? 2 at a given place and time for a given
particle determines the probability of finding
the particle there at that time.
? 2 is called the probability density of the
particle.
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The Uncertainty Principle
If a moving particle is a wave, then there are
limits on the accuracy of the measurements of its
position and speed.
The particle may be located anywhere within the
wave packet at a given time. The maximum of ? 2
is in the middle of the packet. However, the
particle can be found anywhere that ? 2 ? 0.
The uncertainty principle It is impossible to
know both the exact position and the exact
momentum of a particle at the same time.
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The Uncertainty Principle
?x ? precision of position measurement ?px ?
precision of linear momentum measurement h ?
Planck constant
?x ?px ? h/4?
?E ?t ? h/4?
Another form of the uncertainty principle Energy
of a particle can be uncertain for a period of
time ?t h/ (4? ?E).
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Summary
Matter can also behave as a wave, like
electromagnetic waves can behave as
particles. The uncertainty principle implies
that we cannot know future for sure because we
cannot know the present for sure. Importance of
the subject
Brief history of quantum mechanics