Lecture 22Quantum Physics II

Chapter 27.6 27.9

Outline

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

Matter WavesIn 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 momentumLater 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 px h/4x precision of position

measurementpx precision of linear

momentum measurementh Planck constant

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).

SummaryMatter 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