Solve Hermite Equation & Find Its Use in Math Physics

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Discussion Overview

The discussion revolves around the Hermite equation, its solutions, and potential applications in mathematics and physics. Participants explore the relationship between the Hermite equation and the Schrödinger equation, particularly in the context of quantum mechanics.

Discussion Character

  • Exploratory
  • Technical explanation
  • Homework-related

Main Points Raised

  • One participant expresses difficulty in finding a practical application for the Hermite equation, particularly in physics.
  • Another participant suggests that the Hermite equation relates to the Schrödinger equation for a particle in a harmonic potential, indicating that solutions involve Hermite polynomials.
  • A request is made for the series solution to the Hermite equation, along with clarification on how it connects to the Schrödinger equation.
  • A later reply challenges the initial claim of having "done everything" by providing a link to a resource that offers the series solution to the Hermite equation.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the applications of the Hermite equation, and there are multiple viewpoints regarding its connection to the Schrödinger equation and the nature of its solutions.

Contextual Notes

There are limitations in the discussion regarding the assumptions made about the applicability of the Hermite equation and the specific context of its use in quantum mechanics. The connection to the Schrödinger equation remains partially explored.

darkone1687
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I have a problem for a Math Physics course, that I was suppose to find the Hermite equation, find solutions to it, plug them into see if they work, and lastly find a use for the Hermite equation. I've done everything but I can't find a use for the equation I looked almost everywhere I would really applicate the help if someone could give me a use for the equation, it would be best if it was used in physics but if not it's alright. THANK YOU for the help!
 
Physics news on Phys.org
Hermite Equation as in the differential equation producing the Hermite polynomials?

For the case of a particle in a harmonic potential ([itex]\frac{1}{2}m\omega^2x^2[/itex]) in quantum mechanics, the Schrödinger Equation (once rescaled to be in terms of nondimensional variables) has solutions which are proportional to [itex]\exp[-x^2/2][/itex] times the Hermite polynomials.

http://en.wikipedia.org/wiki/Hermite_polynomials
 
I can't find the series solution to this equation can someone post it here please, also I was wondering how it fit in with shrodingers equation I'm suppose to somehow use Hermite to get to Schrödinger, or vice versa?
 

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