Hermite representation for integrals?

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Discussion Overview

The discussion revolves around the representation of Hermite polynomials in integrals, particularly in the context of calculating expectation values for harmonic oscillator wavefunctions. Participants explore the necessity of explicit forms of Hermite polynomials within integrals and the separation of integrals involving multiple variables.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested, Mathematical reasoning

Main Points Raised

  • One participant questions how to incorporate the Hermite polynomial of nth degree into an integral for expectation values, seeking clarity on its representation.
  • Another participant suggests that the explicit form of the Hermite polynomial may not be necessary, arguing that simply using H_n(x) suffices.
  • A participant provides links to resources that may help clarify the topic, including examples of Hermite polynomials.
  • There is a query regarding the separation of integrals involving multiple variables, with a participant proposing a specific form of separation for an integral involving z, x, and y.

Areas of Agreement / Disagreement

Participants express differing views on the necessity of the explicit form of Hermite polynomials in integrals, indicating a lack of consensus on this point. Additionally, the discussion on integral separation remains unresolved, with no clear agreement on the validity of the proposed separation method.

Contextual Notes

Participants do not fully explore the implications of their assumptions regarding the representation of Hermite polynomials or the conditions under which integral separation may hold true. There are also references to external resources that may contain additional context or examples.

Who May Find This Useful

Individuals interested in quantum mechanics, particularly those studying harmonic oscillators and the mathematical properties of Hermite polynomials, may find this discussion relevant.

Mniazi
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Suppose I want an expectation value of a harmonic oscillator wavefunction, then in what way will I write the Hermite polynomial of nth degree into the integral? I have a link of the representation, but don't know what to do with them? http://dlmf.nist.gov/18.3
 
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Why do you need the explicit form inside the integral? Leaving just H_n (x) is more than enough.
 
This gives you the first few...
http://www.bsu.edu/libraries/virtualpress/mathexchange/07-01/HermitePolynomials.pdf
 
ok If I have a integral like $$\int_{-\inf}^{\inf}{z*x*y}$$

then can I write them separately as:

$$\int_{-\inf}^{\inf}{z}*\int_{-\inf}^{\inf}{x}*\int_{-\inf}^{\inf}{y}$$
 

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