SUMMARY
The discussion focuses on finding solutions for the three-dimensional Schrödinger Equation (SE). Users highlight the lack of general procedures for solving the 3D SE and suggest that specific systems, such as those with spherical symmetry, can be approached using spherical coordinates. A notable reference is the article "New method for solving three-dimensional Schrödinger equation" by V. S. Melezhik, published in Il Nuovo Cimento B, which discusses numerical methods but is behind a paywall. Participants recommend searching free archives like arXiv for accessible research papers.
PREREQUISITES
- Understanding of the Schrödinger Equation and its applications in quantum mechanics.
- Familiarity with spherical coordinates and their use in solving differential equations.
- Knowledge of numerical methods for solving partial differential equations.
- Experience with academic research databases and archives, particularly arXiv.
NEXT STEPS
- Research numerical methods for solving the Schrödinger Equation, focusing on finite difference and spectral methods.
- Explore the use of spherical coordinates in quantum mechanics, particularly for systems with spherical symmetry.
- Investigate the arXiv repository for free access to relevant physics papers and methodologies.
- Study the specific case of the hydrogen atom as a benchmark for solving the 3D Schrödinger Equation.
USEFUL FOR
Physicists, quantum mechanics students, and researchers seeking to solve the three-dimensional Schrödinger Equation, particularly those interested in numerical methods and theoretical frameworks.