Quantum Physics Approximation Methods
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Quantum Physics Approximation Methods

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Questions and Answers

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?

  • Time-dependent perturbation theory (correct)
  • WKB method
  • Variational method
  • Time-independent perturbation theory
  • 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?

    <p>Ensures conservation of angular momentum</p> Signup and view all the answers

    In the n=2 case, how many nonzero elements result from the condition 0 = ± 1?

    <p>Two</p> Signup and view all the answers

    What determines the first-order correction in energy of the first state of the hydrogen atom?

    <p>Angular momentum</p> Signup and view all the answers

    What property restricts the nonzero matrix elements to h2, 1, 0 | z | 2, 0, 0i in the n=2 case?

    <p>Angular momentum conservation</p> Signup and view all the answers

    Which effect arises from the exchange of photons with spin 1?

    <p>Stark effect</p> Signup and view all the answers

    Which method is used to calculate the fine structure corrections in the hydrogen atom?

    <p>WKB method</p> Signup and view all the answers

    What contributes to the four-fold degeneracy in the n=2 case?

    <p>Interaction with magnetic field</p> Signup and view all the answers

    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, , m is required
    • Lz and z commute, so [Lz, z] = 0
    • m = m0 for non-zero matrix elements
    • 0, rather 0 = ± 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), m i

    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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    Description

    This quiz covers topics in quantum physics approximation methods, including time independent perturbation theory, time dependent perturbation theory, variational method, and WKB method. It also discusses fine structure, the hydrogen atom, Zeeman Effect, Stark Effect, and a historical overview of important figures and discoveries in quantum physics.

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