Question

What is the physical meaning of the following with relations and diagrams.
1-Zero point energy   
2- Thermal expansion  
3- The dispersion relation
4-Hall Effect       
5- The density of states    
6- Debye T^(3 ) Law

Answer 1

1. Zero energy is the lowest energy of a quantum mechanical system. Now classically it should be zero. But in quantum mechanics it is never zero as a system should have a minimum energy to sustain itself.

2. When a system is heated it's length or area or volume changes(usually increases) . It is known as thermal expansion. When a system is heated, due to heat energy the molecules and atoms starts vibrating and their equilibrium distance changes(usually increases). This is reason behind thermal expansion.

3. Dispersion relation basically describes behaviour of a wave in a medium. It relates the wavelength of a wave with it's frequency. For Linnear relationship (for a continuous medium) the relation is w=kc, where w is frequency, k is 2π/, where lamda is wavelength.

4. Hall effect is basically production of potential difference of a electrical conductor when a magnetic field is applied in a direction perpendicular to that of flow of current. Metals also show Hall effect but they have a really small Hall coefficient.

5. Density of states is number of electronic energy level per unit volume at a particular energy state. So high Density of states means that there are many energy levels to occupy in a unit volume. It is directed related to Dispersion relation.

6. The heat capacity predicted by Debye says that at low temperatures specific heat is proportional to T^3. Which is known as Debye T^3 law. At high temperatures specific heat dependence of solid is predicted correctly by both Einstein model and Debye Model but at low temperature Einstein predicts exponential freezing which is experimentally incorrect and Debye T^3 law explains it correctly.