# Study Guide:Mathematical Mesoscopic Physics/Physics Prerequisites

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This is a brief list of topics you should learn about before even turning to mesoscopic physics proper. These are things that physics students learn during their courses on quantum mechanics (QM I and II), thermodynamics and statistical physics, and electrodynamics. However, since we have selected only the subset that comprises the bare essentials you need to know, the amount of this material is much smaller than you might expect.

## Basic material from a first quantum mechanics course[edit]

- Schrödinger equation for one particle (time-dependent/-independent)
- Energy levels as eigenvalues of the Hamiltonian operator (Hamiltonian (Wikipedia)), and energy eigenstates
- Free evolution, wave packets (useful for semiclassics!)
- Heisenberg's uncertainty relation

## More advanced material to deal with many particles and thermodynamic equilibrium[edit]

- Boltzmann distribution, partition sum
- Density matrix
- Basis in a many-body Hilbert space ("occupation numbers")
- Fermi-Dirac distribution, chemical potential, Fermi surface
- Second quantization