Where Can I Find Solutions for 3D Schrödinger Equation?

Click For Summary
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.

Radiance
Messages
2
Reaction score
0
Hello everyone! I am a new member and please sorry for some question that perhaps were discussed here before. But really I need your help. I am searching for methods of solving 3 dimensional Schrödinger equation. Till now in internet I coulnd't find any solution. All the papers and articles are either about 1 dimensional equation or this topic is discussed just in some article that you should pay for reading them. It is several months I am trying to find it and I am going to loose my hope. Perhaps any of you can advise some software that could be used for solving 3 dimensional equation or just can advise me an algorithm? I will be so thankfull for any help :!)

Olga
 
Physics news on Phys.org
There's not a general procedure for solving the 3D Schrödinger Equation (SE). I think you will get better responses if you describe for what kind of system you are trying to solve the 3D SE.

For systems with spherical symmetry (atoms, for example) you could rewrite the SE in spherical coordinates and take advantage of the symmetry. It gets very complicated for anything larger than the hydrogen atom though so that approximations need to be used.
 
thanks a lot for your reply. I am searching for numerical method of solving Schrödinger Equation, I know there is no general method.
There are some articles that describe such problem like

New method for solving three-dimensional Schrödinger equation
Authors:
Melezhik, V. S.
Publication:
Il Nuovo Cimento B, Vol. 106, p.537 (NCimB Homepage)
Publication Date:
00/1991
Origin:
ADS
Bibliographic Code:
1991NCimB.106..537M
but of course it is not possible to read them
 
Try searching the free archives first (e.g. http://xxx.lanl.gov/). Since the early 1990's many, if not most, physics papers have been posted there before appearing in other journals.
 

Similar threads

Replies
29
Views
2K
  • · Replies 5 ·
Replies
5
Views
2K
Replies
1
Views
2K
Replies
2
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
Replies
6
Views
2K
Replies
1
Views
3K
  • · Replies 1 ·
Replies
1
Views
2K
Replies
3
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K