Differential equation Hermite polynomials

Click For Summary
SUMMARY

The discussion centers on solving a differential equation of the form F''(x) + (Cx² + D)F(x) = 0, which is identified as the ordinary differential equation (ODE) for Hermite polynomials. The user successfully applied an ansatz using Hermite polynomials to find a solution to the equation. This confirms the relationship between the differential equation and Hermite polynomials in quantum physics applications.

PREREQUISITES
  • Understanding of ordinary differential equations (ODEs)
  • Familiarity with Hermite polynomials
  • Basic knowledge of quantum physics concepts
  • Experience with mathematical methods in physics
NEXT STEPS
  • Study the properties and applications of Hermite polynomials in quantum mechanics
  • Explore techniques for solving ordinary differential equations
  • Learn about the role of differential equations in quantum physics
  • Investigate the method of ansatz in solving differential equations
USEFUL FOR

Students and professionals in physics, mathematicians, and anyone interested in solving differential equations related to quantum mechanics.

dakold
Messages
13
Reaction score
0
I got a problem in quantum physics that i have come to a differential equation but I don't see how to solve it, its on the form
F''(x)+(Cx^2+D)F(x)=0.
How should I solve it?
Thanks
 
Physics news on Phys.org
Isn't this the ODE for the Hermite polynomials ?
 
yes it's. i tried to make a ansatz with hermite polynomials and it solved the equation.
 

Similar threads

  • · Replies 18 ·
Replies
18
Views
6K
  • · Replies 7 ·
Replies
7
Views
2K
Replies
19
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
Replies
26
Views
3K
Replies
10
Views
2K
Replies
9
Views
3K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K
Replies
3
Views
2K