## Direct admission at the second year is authorized in Paris and allows the delivery of UPMC master diploma

### Only valid in Paris

Students must fill the admission criteria mentioned for the first year (link to first year admission) and in addition justify the following prerequisites:

· Quantum mechanics, atomic and molecular physics :Hydrogen atom: radial and angular components of the wavefunction, Periodic table, Hund's rule, Hydrogen molecule, Static perturbations (degenerated and non-degenerated cases), Variational method, Kinetic orbital momentum

· Statistical Physics: Concept of thermodynamic potential. Legendre transformations. Partition function. Entropy, Quantum statistics: Fermi-Dirac and Bose-Einstein

· Electrodynamics: Electrodynamics of continuous media, Complex refractive index. Absorption and reflection.

· Basic Solid State Physics: Crystal symmetries. Bravais lattices. X-ray diffraction. Electronic and ionic degrees of freedom: Born-Oppenheimer approximation. Phonons in 1D periodic systems: Brillouin zone. Dynamical matrix. Acoustic and optical branches. Electronic band structure. Bloch functions

· Mathematics: Fourier transforms and delta function, Basics of functionals and functional derivatives

· Programming Language: Fortran 95 or C

### Language requirements :

No proficiency in languages required.