Method for solving complex equations f(z)=0

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SUMMARY

The discussion focuses on methods for solving complex equations of one complex variable, specifically highlighting Newton's method as a viable option. While Newton's method is effective, it requires a first approximation and does not guarantee all solutions, which is a limitation for the user's needs in calculating resonance energies for a Bachelor Thesis in Quantum Mechanics. The user also explored real function methods, such as the bisection method and Ridder's Method, which proved successful for integrating the Schrödinger Equations and obtaining eigenvalues.

PREREQUISITES
  • Understanding of complex variable theory
  • Familiarity with Newton's method for root-finding
  • Knowledge of bisection method and Ridder's Method
  • Basic principles of Quantum Mechanics and Schrödinger Equations
NEXT STEPS
  • Research advanced techniques for solving complex equations, such as Durand-Kerner method
  • Learn about numerical methods for eigenvalue problems in Quantum Mechanics
  • Explore the use of software tools like MATLAB for complex equation solving
  • Investigate alternative root-finding algorithms, such as Bairstow's method
USEFUL FOR

Students and researchers in Quantum Mechanics, mathematicians focusing on complex analysis, and anyone interested in numerical methods for solving complex equations.

liviuct
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Hey! Does anyone know any good method for solving complex equations of one complex variable? I found over the internet that I could use Newton's method, and I tried it for a common function, and it worked. Anyway, I'm not very pleased of Newton's method because of the use of the first aproximation value. Also it does not return all the solutions. I need it for calculating some resonances energies for my Bachelor Thesis in Quantum Mechanics.
I also tried methods for real functions (in order to integrate the Schrödinger Equations and obtaining the eigenvalues), like bisection method or Ridder's Method. They worked just fine.

Thank you.
 
Physics news on Phys.org
For most equations you need a guess as an approximate solution or a bracket. Which method works best tends to be problem specific.
 

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