What is the General Solution for the Schrödinger Equation in a 2D or 3D Box?

In summary, the Schrödinger equation is a fundamental equation in quantum mechanics that describes the changes in the quantum state of a physical system over time. It was developed by Austrian physicist Erwin Schrödinger in 1926 and has been significant in enabling scientists to predict the behavior of particles on a microscopic scale. The equation can be solved using various mathematical techniques, and has numerous applications in fields such as quantum chemistry, solid state physics, and quantum technologies.
  • #1
kasse
384
1
The solution of the one dimensional Schrödinger equation for a particle in a one dimensional box is [tex]Asin \frac{n \pi x}{a}[/tex]. But how about if the box is 2D or 3D?
 
Physics news on Phys.org
  • #2
Have you considered actually solving the Schroedinger equation for these cases?...An attempt at that would probably be a good way to start.
 
  • #3
What is the general solution then?
 
  • #4
kasse said:
What is the general solution then?

Show us an attempt and I'll be happy to help you. Start with the 2D case.
 

Related to What is the General Solution for the Schrödinger Equation in a 2D or 3D Box?

1. What is the Schrödinger equation?

The Schrödinger equation is a mathematical equation that describes how the quantum state of a physical system changes over time. It is a fundamental equation in quantum mechanics and is used to predict the behavior of particles on a microscopic scale.

2. Who developed the Schrödinger equation?

The Schrödinger equation was developed by Austrian physicist Erwin Schrödinger in 1926. He received a Nobel Prize in Physics in 1933 for his contributions to the development of quantum mechanics.

3. What is the significance of the Schrödinger equation in quantum mechanics?

The Schrödinger equation is significant because it provides a mathematical framework for understanding the behavior of particles on a microscopic scale. It allows scientists to make predictions about the behavior of particles and has been used to develop technologies such as transistors and lasers.

4. How is the Schrödinger equation solved?

The Schrödinger equation is a complex mathematical equation that can be solved using various mathematical techniques, such as separation of variables and perturbation theory. In some cases, an analytical solution cannot be found and numerical methods are used to approximate the solution.

5. What are some applications of the Schrödinger equation?

The Schrödinger equation has many applications in areas such as quantum chemistry, solid state physics, and nuclear physics. It is also used in the development of quantum technologies, such as quantum computing and quantum cryptography.

Similar threads

  • Advanced Physics Homework Help
Replies
1
Views
731
  • Advanced Physics Homework Help
Replies
29
Views
262
  • Advanced Physics Homework Help
Replies
1
Views
303
  • Advanced Physics Homework Help
Replies
5
Views
1K
  • Advanced Physics Homework Help
Replies
1
Views
748
  • Advanced Physics Homework Help
Replies
1
Views
934
  • Advanced Physics Homework Help
Replies
2
Views
995
Replies
1
Views
641
  • Advanced Physics Homework Help
Replies
4
Views
1K
  • Advanced Physics Homework Help
Replies
2
Views
2K
Back
Top