{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# ex08 - Solid State Theory Exercise 8 FS 11 Prof M Sigrist...

This preview shows pages 1–2. Sign up to view the full content.

Solid State Theory Exercise 8 FS 11 Prof. M. Sigrist Exercise 8.1 Bohr-van-Leeuwen-Theorem Prove the Bohr-van-Leeuwen-theorem, which states that there is no diamagnetism in classical physics. Hint: H ( p 1 , . . . , p N ; q 1 , . . . , q N ) is the Hamiltonian of the N -particle system with vanish- ing external magnetic field. In comparison, the Hamiltonian with applied magnetic field B is then given by H ( p 1 - e/cA 1 , . . . , p N - e/cA N ; q 1 , . . . , q N ), where B = ∇ × A and A i = A ( q i ). The magnetization can be calculated using M = - H ∂B = 1 β log Z ∂B , (1) with the partition function Z of the system in the magnetic field. Exercise 8.2 Landau Diamagnetism Calculate the orbital part of the magnetization of the free electron gas in 3D in the limits of low temperature and small external field ( T 0 , H 0). In addition, show that the magnetic susceptibility at T = 0 and H = 0 is given by χ = - 1 3 m 2 m * 2 χ P , (2) where χ P is the Pauli (spin-)susceptibility.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 2

ex08 - Solid State Theory Exercise 8 FS 11 Prof M Sigrist...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online