Schrodinger Equation in 3 dimension

Click For Summary
SUMMARY

The discussion focuses on solving the Schrödinger equation in three dimensions, particularly in the context of spherically symmetric potentials. Participants emphasize the importance of quantum mechanics texts that detail the separation of the equation into radial and angular components. It is noted that for arbitrary potentials, closed-form solutions to the radial equation may not exist, complicating the derivation of spherical harmonics and radial equations. Online resources regarding ordinary differential equations are also recommended for further understanding.

PREREQUISITES
  • Understanding of quantum mechanics principles
  • Familiarity with the Schrödinger equation
  • Knowledge of spherical harmonics
  • Basic concepts of ordinary differential equations
NEXT STEPS
  • Study quantum mechanics texts that cover the separation of variables in the Schrödinger equation
  • Research the derivation of spherical harmonics in quantum mechanics
  • Explore resources on solving ordinary differential equations
  • Investigate specific examples of spherically symmetric potentials in quantum systems
USEFUL FOR

Students and researchers in physics, particularly those focusing on quantum mechanics and mathematical methods in physics, will benefit from this discussion.

sciboudy
Messages
89
Reaction score
0
How can i solve Schrödinger equation in 3dimension i want to know how can i deduce every equation ? and how can i find equation of spherical harmonic and radial equation ?
i need to understand this proof
 
Physics news on Phys.org
i know it's so hard
 
Any decent quantum mechanics text explains how to separate Schrödinger's equation into a radial and angular part when the potential is spherically symmetric. If there's some specific step that is challenging you, please post about it.

For an arbitrary potential, there is no reason to expect a closed-form solution to the radial equation to exist, so it's impossible to answer your question. There are some online resources about ordinary differential equations listed in https://www.physicsforums.com/showthread.php?t=110274&highlight=differential+equations
 

Similar threads

  • · Replies 39 ·
2
Replies
39
Views
2K
  • · Replies 8 ·
Replies
8
Views
2K
  • · Replies 3 ·
Replies
3
Views
690
  • · Replies 9 ·
Replies
9
Views
3K
  • · Replies 2 ·
Replies
2
Views
1K
  • · Replies 17 ·
Replies
17
Views
3K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 143 ·
5
Replies
143
Views
11K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 11 ·
Replies
11
Views
2K