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

2. 7.1. Quantum States in Square Well
1-D square-well potential :
Bound states energies E =  EB > 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

5. Ex :

6. 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 | fi+1 | > | f i | ) may be helpful.
Tips:

8. Ex :