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Questions and Answers
Why is 0 equal to ±1 in the context of Stark effect?
Why is 0 equal to ±1 in the context of Stark effect?
- To conserve angular momentum (correct)
- To cause four-fold degeneracy
- To maintain energy balance
- To prevent Zeeman effect
Which perturbation theory method deals with time-dependent interactions?
Which perturbation theory method deals with time-dependent interactions?
- Time-dependent perturbation theory (correct)
- WKB method
- Variational method
- Time-independent perturbation theory
What causes the Stark effect according to the given text?
What causes the Stark effect according to the given text?
- Interaction between electric dipole and electric charge (correct)
- Variational method
- WKB method
- Zeeman effect
What is the significance of the condition m = m0?
What is the significance of the condition m = m0?
In the n=2 case, how many nonzero elements result from the condition 0 = ± 1?
In the n=2 case, how many nonzero elements result from the condition 0 = ± 1?
What determines the first-order correction in energy of the first state of the hydrogen atom?
What determines the first-order correction in energy of the first state of the hydrogen atom?
What property restricts the nonzero matrix elements to h2, 1, 0 | z | 2, 0, 0i in the n=2 case?
What property restricts the nonzero matrix elements to h2, 1, 0 | z | 2, 0, 0i in the n=2 case?
Which effect arises from the exchange of photons with spin 1?
Which effect arises from the exchange of photons with spin 1?
Which method is used to calculate the fine structure corrections in the hydrogen atom?
Which method is used to calculate the fine structure corrections in the hydrogen atom?
What contributes to the four-fold degeneracy in the n=2 case?
What contributes to the four-fold degeneracy in the n=2 case?
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Study Notes
Approximation Methods in Physics
- Time-independent perturbation theory
- Time-dependent perturbation theory
- Variational method
- WKB method
Fine Structure and Hydrogen Atom
- Hydrogen atom has fine structure due to interactions
- Energy levels of hydrogen atom are affected by external electric field (Stark effect)
Stark Effect
- Electric analogue of Zeeman effect
- Hydrogen atom develops an electric dipole moment in an external electric field
- Energy levels of hydrogen atom split due to Stark effect
- Additional term HStark in the Hamiltonian of H-atom
Hydrogen Atom under Electric Field
- Constant and uniform electric field ∊ in z-direction
- HStark = -|e|∊z
Energy Correction due to Stark Effect
- Expectation value of HStark in the state |n,
, mis required - Lz and z commute, so [Lz, z] = 0
- m
= m0 for non-zero matrix elements â‰0, rather0 =± 1
Selection Rule for Stark Effect
0 =± 1 due to electric dipole interacting with electric field by exchanging photons with spin 1- Angular momentum of electron decreases or increases by 1 only
Matrix Elements for Stark Effect
- Non-zero matrix elements of the form: hn,
, m| z | n0, (± 1), mi
Example: Ground State of H-Atom
- First-order correction in energy: E1,0,0 = 0, since
0 =
n=2 Case
- Four-fold degenerate: |2, 0, 0i , |2, 1, 1i , |2, 1, 0i , and |2, 1, −1i
- Non-zero elements: h2, 1, 0 | z | 2, 0, 0i and h2, 0, 0 | z | 2, 1, 0i
- First-order correction in energy: E2,
,m= ±|e|a0 ε
Historical Overview
- Johannes Stark (1874-1957) - Physics Nobel Prize (1919)
- Antonino Lo Surdo (Italy, 1913) - observed the same effect, known as Stark-Lo Surdo effect
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