Bohr–van Leeuwen theorem
The Bohr -van Leeuwen theorem, is a theorem in the field of solid state physics and statistical physics. It states that when applying the classical statistics, the magnetization in thermal equilibrium would be zero, since the kinetic energy of a charge in a magnetic field does not change. Thus, magnetism is a purely quantum mechanical effect in solids.
Heuristic classic view
The magnetization (the number of magnetic moments per unit volume ) is proportional to the change in the energy of a system in a magnetic field. Since the force on a moving charge ( Lorentz force ) acting exactly perpendicular to the moving direction of the charge, said charge undergoes through the field, although a change in direction, the absolute value remains constant, i.e., the change of the power is zero, and thus the magnetization.
Mathematical Proof
A charged particle in a magnetic field with vector potential is defined by the Hamiltonian, the first argument is the so-called kinetic momentum.
The partition function of a system of N such ( indistinguishable ) particles in statistical physics classically defined on this being treated in three dimensions.
Now substituting. Since all the pulses over the entire area to be integrated, the integral limits not change. The partition function then becomes As this is now clearly no longer the vector potential and thus not dependent on the external magnetic field, the magnetization disappears,
Where F is the free energy