Where Can I Find Solutions for 3D Schrödinger Equation?

In summary, the individual is a new member seeking help with finding methods for solving the 3 dimensional Schrödinger equation. They have been unsuccessful in finding solutions online and are asking for recommendations for software or algorithms. They mention a specific article discussing the problem, but are unable to access it. Other members suggest utilizing spherical symmetry for systems with atoms and searching free archives for physics papers.
  • #1
Radiance
2
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
 
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  • #2
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.
 
  • #3
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
 
  • #4
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.
 

What is the Schrödinger equation?

The Schrödinger equation is a mathematical formula that describes the behavior of quantum particles, such as electrons, in a given system. It was developed by Austrian physicist Erwin Schrödinger in 1925 and is a fundamental equation in quantum mechanics.

What is the significance of the Schrödinger equation?

The Schrödinger equation is significant because it allows us to make predictions about the behavior of quantum systems. It has been used to explain various phenomena, such as the behavior of atoms, molecules, and subatomic particles, and has played a crucial role in the development of modern technology.

How is the Schrödinger equation used in quantum mechanics?

The Schrödinger equation is used to calculate the probability of finding a particle in a certain location or state. It is also used to determine the energy levels of a system and how they change over time. Additionally, the Schrödinger equation is used to study the wave-like properties of particles and their interactions with other particles.

What are the key components of the Schrödinger equation?

The Schrödinger equation includes a wave function, which describes the state of a quantum system, and an operator, which represents the physical properties being measured. It also includes the Hamiltonian, which represents the total energy of the system, and the time variable, which allows us to track changes in the system over time.

Are there any limitations to the Schrödinger equation?

While the Schrödinger equation has been successful in describing the behavior of many quantum systems, it does have some limitations. For example, it does not account for relativistic effects, and it cannot be applied to systems with strong interactions between particles. In these cases, more advanced equations, such as the Dirac equation, are needed.

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