Quantum mechanics

Look at lecture notes for diagrams - very useful

Things that proved classical mechanics wrong

• Waves can behave as particles - light waves are affected by gravity therefore they have mass; shining a light on a metal surface can provide a measurable force therefore light has momentum and therefore has mass.

• The energy of light does not depend on its intensity but its wavelength - long wavelengths of light do not excite eject electrons when shone on metal, no matter the intensity, but after a certain critical value, shorter wavelengths will eject electrons.

• Particles can behave as waves - subatomic particles, hydrogen nuclei etc can be diffracted and give the same diffraction pattern as if light were used. They can also interact with each other constructively and destructively - C60 can do this.

• Particles do not possess continuously varying energy - they can have energies at specific discrete levels

What is a wavefunction

The resulting wave from the interference of a collection of waves - CHECK IN TEXTBOOK

What is a wave-packet

A particle - a collection of waves

How to calculate intensity of a wavefunction

The square of the wavefunction at any point in space

Born interpretation

For a classical particle (e.g. electron) the square of the wavefunction - i.e. intensity - can be interpreted as the probability of finding the particle at that point. To do this, wavefunctions usually have to be normalised, so that the total intensity is 1.

How to increase the resolution on an electron microscope

Speed up the electrons - this makes the wavelength shorter

Heisenberg’s uncertainty principle

It is impossible to know both the energy and the precision of a particle at the same time. This is because: a pure wave has no position and a pure particle has a completely undefined energy (because it has no wavelength). A wave packet has an approximate position (but it is spread out so does not have an absolute position) and an approximate energy (because the wavelength and so frequency changes). If you measure one, you cannot measure the other.

Zero point energy

A particle cannot have no energy: if a particle was completely still then both its energy (zero) and its position would be completely known - this contradicts the Uncertainty Principle so it cannot be true.

For a particle in a box, what are the allowed wavelengths

Anything that would make the amplitude of the wave 0 at each end of the box.

What happens when a wave reaches the end of the box

Both its amplitude and phase are reflected (i.e. the would-be path of the wave is reflected in the y axis and then that is reflected in the x axis)