7 Additional interactions in atoms Flashcards
(26 cards)
What is the classical angular momentum?
I = Mωr2
What is the equation for magnetic moment?
μ = j×A = -el/2M
Where l is the angular momentum
What is the equation for the change of energy in a given state?
ΔE = μBBm
With μB the Bohr magneton
What is equation for a component of the force of a magnetic moment?
F = - μz ∂B/∂z
How does angular momentum add up in QM?
l1 ⊕ l2 = |l1 - l2|
What is the spin of an electron?
1/2
What is the definition of Hermitian conjugation?
A♱ = AT*
Taking the transpose then complex conjugate
What is the x Pauli spin matrix?
σx =
(0 1)
(1 0)
What are the is the y Pauli spin matrix?
σy =
(0 -i)
(i 0)
What are the is the z Pauli spin matrix?
σz =
(1 0)
(1 -1)
What is the spin /12 operator?
Si = ℏσi/2
How do we find eignenvalues?
det(M-λ)=0
Where M is the matrix and λ =
(λ 0)
(0 λ)
What is the result of the Pauli exclusion principle?
Two fermions cannot be in the same quantum state
What is the equation for total angular momentum?
j = l+s
What is the contribution to the Hamiltonian operator from angular momentum?
HLS = f(r)(J2 -L2 -S2)
What is the equation for the Hamiltonian operator for magnetic moments?
HB = -eB0/2M (Lz+2Sz)
What is the equation for the correction of the energy of the states for a hydrogen atom?
ΔH = HLS + HB
What is the strong field Zeeman effect?
The HB term dominates over the HLS term
What is the correction to the energy for the strong field Zeeman effect?
ΔE = eℏB0/2M (ml + 2ms)
What is the direction of the magnetic field for the strong field Zeeman effct?
Aligned with the z axis
What is the energy correction for the weak field Zeeman effect?
δE = gμBmjB
What is the equation for the Bohr magneton?
μB = eℏ/2M
What are the three regimes regarding magnetic field?
No external magnetic field
Rising external magnetic field
Very high external magnetic field
What happens to the energy levels with no external magnetic field?
Energy levels split to two
