A hydrogen atom is placed in a uniform magnetic field B₀ = B₀ Ẑ (the Hamiltonian can be written as in Equation 4.230). Use the Feynman– Hellman theorem (Problem 7.38) to show that

where the electron’s magnetic dipole moment (orbital plus spin) is

The mechanical angular momentum is defined in Equation 4.231.
Note: From Equation 7.114 it follows that the magnetic susceptibility of N atoms in a volume V and at 0 K (when they’re all in the ground state) is

where E₀ is the ground-state energy. Although we derived Equation 7.114 for a hydrogen atom, the expression applies to multi-electron atoms as well—even when electron–electron interactions are included.

Transcribed Image Text:

HE, а во = - (Wn \Mz Wп) (7.114)