Unit 3: Spin, Ang. Mom., Approx.

Question 1

Spectral Lines and Angular Quantum Numbers

Answer 1

Question 2

Lifted Degeneracy

Answer 2

Question 3

Spin-Orbit Coupling

Answer 3

Question 4

Zeeman Effects:

Answer 4

Question 5

Zeeman Effects (Teslas Approximates):

Answer 5

Question 6

Orbital Angular Momentum:

Answer 6

Question 7

Lorentz Force

Answer 7

Question 8

Orbital Magnetic Moment

Answer 8

Question 9

Torque due to Moment:

Answer 9

Question 10

Work done (due to orbital angular momentum):

Answer 10

Question 11

Spin Magnetic Moment:

Answer 11

Question 12

Work done (due to spin magnetic moment)

Answer 12

Question 13

Zeeman Energy Term

Answer 13

Question 14

Origin of Magnetic Field (S.O.C.)

Answer 14

Question 15

Energy contribution from spin-orbit coupling

Answer 15

Question 16

Total Potential Energy Expression
- includes spin-orbit, zeeman effect, and electron-nucleus interaction

Answer 16

Question 17

Hamiltonian Modification

Answer 17

Question 18

Energy correction due to Perturbation

Answer 18

Question 19

Perturbation Theory (definition)

Answer 19

Question 20

Perturbed Hamiltonian
- Includes spin-orbit coupling and Zeeman effect

Answer 20

Question 21

Energy Expression
(Including Internal and External Magnetic Fields)

Answer 21

Question 22

Spin-Orbit Coupling Operator

Answer 22

Question 23

Quantum Operators for Angular Momentum

Answer 23

Question 24

Spin-Orbit Energy Contribution

Answer 24

Question 25

Energy Correction Due to Perturbation

Answer 25

Question 26

Energy Difference Between Two Levels
(Selection Rule Included)

Answer 26

Question 27

Fine Structure Constant

Answer 27

Question 28

Energy Shift Due to Zeeman Effect

Answer 28

Question 29

Weak-Field Zeeman Effect
- The perturbing Hamiltonian in the weak-field limit

Answer 29

Question 30

Landé g-factor Expression
- where the Landé g-factor accounts for the combined orbital and spin contributions to magnetic moment

Answer 30

Question 31

Photon Angular Momentum Conservation Statement

Answer 31

Question 32

Small correction statement
(For small field)

Answer 32

Question 33

Perturbation Theory Setup

Answer 33

The Hamiltonian is split into an unperturbed part and a small perturbation

Question 34

Correction of Wavefunctions and Energy Levels

Answer 34

Expansion of wavefunctions and energy levels in terms of perturbation theory:

Question 35

Zeroth and First-Order Energy Corrections

Answer 35

Question 36

The first order energy shift

Answer 36

Question 37

1st Order Energy Correction
- The perturbed energy
- Expectation value calculation

Answer 37

Question 38

Constant Perturbation Assumption
- when given V_0

Answer 38

Question 39

General Result for Coefficients
- Expansion coefficients for the perturbed wavefunction

Answer 39

Question 40

2nd Order Energy Correction
- The second-order energy shift
- substituting a_nk
- Using |H’_nk|^2

Answer 40

Question 41

1st Order Wavefunction Correction
(Full wave function to 1st order)

Answer 41

Question 42

Trial Function (Variation Principle)

Answer 42

Question 43

To find best result for nu(x) and <E></E>

Answer 43