Download Quantum Physics II

Lecture 22
Quantum Physics II
Chapter 27.6  27.9
Outline
• De Broglie Wavelength
• The Electron Microscope
• The Wave Function and The Uncertainty Principle
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
Plank’s 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
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.
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.
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).
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