Cylindrically symmetric potential function

Click For Summary
SUMMARY

The discussion focuses on solving the 3-D Schrödinger equation for a particle in a cylindrically symmetric potential. The central potential function for spherically symmetric cases is defined as V=Ze²/r, but the participants seek to derive the appropriate form for cylindrical symmetry. A key suggestion is to utilize cylindrical coordinates as the initial step in the derivation process.

PREREQUISITES
  • Understanding of the 3-D Schrödinger equation
  • Familiarity with potential functions in quantum mechanics
  • Knowledge of cylindrical coordinates
  • Basic concepts of symmetry in physics
NEXT STEPS
  • Research the derivation of potential functions in cylindrical coordinates
  • Study the application of the Schrödinger equation in non-spherical symmetries
  • Explore quantum mechanics textbooks focusing on potential theory
  • Investigate numerical methods for solving the Schrödinger equation
USEFUL FOR

Students and researchers in quantum mechanics, particularly those studying potential functions and symmetry in physical systems.

Amith2006
Messages
416
Reaction score
2

Homework Statement



I am trying solve the 3-D Schrödinger equation for a particle in a cylindrically symmetric potential. If it was the case of spherically symmetric potential, then we can approximate it to a central potential. But what will be the form of the potential in the cylindrically symmetric case? Can any suggest a way to derive it?

Homework Equations


central potential function is given by,
V=Ze^2/r



The Attempt at a Solution

 
Physics news on Phys.org
Have you tried anything yet?

P.S. The obvious first step is to use cylindrical coordinates ;-)
 

Similar threads

  • · Replies 13 ·
Replies
13
Views
3K
Replies
6
Views
4K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 7 ·
Replies
7
Views
3K
  • · Replies 1 ·
Replies
1
Views
1K
  • · Replies 1 ·
Replies
1
Views
4K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
Replies
11
Views
3K
Replies
3
Views
5K