State the properties of matter waves.

Properties of matter waves (de Broglie waves):

1. Wavelength \(\lambda=\dfrac{h}{p}=\dfrac{h}{mv}\): lighter particles have larger wavelengths, and so do slower ones.
2. If \(v=0\), \(\lambda=\infty\): a wave is associated only with a moving particle.
3. Matter waves are not electromagnetic waves. They are produced by any moving particle, charged or uncharged.
4. Their phase velocity \(v_p=c^2/v\) is greater than the speed of light. It has no physical meaning: the particle travels with the group velocity \(v_g=v\).
5. The wave amplitude \(\psi\) is not directly measurable. \(|\psi|^2\) gives the probability of finding the particle (probability waves).
6. They show diffraction and interference, as in the Davisson–Germer experiment and electron diffraction, which is used in electron microscopes.
7. For a particle accelerated through potential \(V\): \(\lambda=\dfrac{h}{\sqrt{2meV}}\); for an electron \(\lambda=\dfrac{12.27}{\sqrt V}\) Å.