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7.Trial and Error Searching

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7. Trial and Error Searching Quantum States in Square Well Trial and Error Root Finding via Bisection Algorithm Newton-Raphson Algorithm 7.1. Quantum States in Square ... – PowerPoint PPT presentation

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Title: 7.Trial and Error Searching


1
7. Trial and Error Searching
  1. Quantum States in Square Well
  2. Trial and Error Root Finding via Bisection
    Algorithm
  3. Newton-Raphson Algorithm

2
7.1. Quantum States in Square Well
1-D square-well potential
Bound states energies E ? EB gt 0 are given by (
? 2 m a 1)
  • Problem
  • Find several EB ?s for the even wave functions
    with V0 10.
  • See if increasing V0 , say to 20, or 30, may
    produce a larger number of bound states.

3
7.2. Trial and Error Root Finding via Bisection
Algorithm
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Ex. 7.1.
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7.3. Newton-Raphson Algorithm
Let
?
Newton-Raphson algorithm
In case f ? is not known analytically
secant method
  • Initial point must be close to actual solution.
  • Backtracking ( reduce ?x if fi1 gt f i )
    may be helpful.

Tips
7
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8
Ex. 7.2.
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