Question

1.- Write a paragraph of 10 lines about the importance of band structure in quantum mechanics.

2.- Write a paragraph of 10 lines about the importance of band structure in experimental physics.

PD: please be clear with the letters and expressions.

Answer 1

BAND STRUCTURE IN QUANTUM MECHANICS:

1. Band structure describes the quantum-mechanical behavior of electrons in solids.

2. Inside isolated atoms, electrons possess only certain discrete energies, which can be depicted in an energy-level diagram as a series of distinct lines.

3. In a solid, where many atoms sit in close proximity, electrons are “shared.”

4. The equivalent energy level diagram for the collective arrangement of atoms in a solid consists not of discrete levels, but of bands of levels representing nearly a continuum of energy values.

5. In a solid, electrons normally occupy the lowest lying of the energy levels.

6. In conducting solids the next higher energy level (above the highest filled level) is close enough in energy that transitions are allowed, facilitating flow of electrons in the form of a current.

7. In insulating solids the next higher energy level lies far above the highest filled level (separated from it by an energy gap), prohibiting electrical current.

8. Semiconductors are actually insulators, but their conduction is enough that they are classified separately.

9. Their gap lies between those of conductors and insulators; the energy gap is small.

BAND STRUCTURE IN EXPERIMENTAL:

To actually measure the 3D band structure is quite a difficult proposition. In materials that are quasi-2D (materials that are weakly bonded along one axis), the best probe of band structure today is angle-resolved photoemission spectroscopy. However, it only probes the band structure of the occupied states. The unoccupied states' band structure. Quantum oscillation experiments provide valuable information about the Fermi surface, but must be conducted under a large magnetic field, which may itself alter the Fermi surface in some cases. Scanning tunneling microscopy provides valuable information about the density of states of a materials band structure. Optical experiments can yield information about the size of the band gap in insulators. Also, DFT (density functional theory) calculations are routinely performed to estimate band structure in materials. Obviously, these probes can give you more information than the quick description here.

All in all, it must be said that there is no one probe that can provide the band structure of all materials effectively. Most of the time one deduces the characteristics of the band structure from a wealth of experiments and calculations