What are orthogonal wavefunctions?

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Discussion Overview

The discussion revolves around the concept of orthogonal wavefunctions, exploring their definition and implications in the context of quantum mechanics and linear algebra. Participants seek to understand how the mathematical notion of orthogonality applies to wavefunctions and their physical significance.

Discussion Character

  • Conceptual clarification, Technical explanation

Main Points Raised

  • One participant expresses a basic understanding of orthogonality in terms of vectors and seeks clarification on its application to wavefunctions.
  • Another participant explains that orthogonality in wavefunctions can be understood through the concept of an inner product, which generalizes the dot product, and provides an integral representation of this inner product.
  • A later contribution states that orthogonal wavefunctions correspond to mutually exclusive physical states, suggesting a link between the mathematical concept and its physical interpretation.

Areas of Agreement / Disagreement

Participants appear to agree on the basic definition of orthogonality and its mathematical representation, but the discussion does not resolve the broader implications or interpretations of orthogonal wavefunctions in physical contexts.

Contextual Notes

The discussion does not address specific assumptions or limitations regarding the definitions of wavefunctions or the contexts in which orthogonality is applied.

lms_89
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I know what orthogonal means (well, I know orthogonal vectors are perpendicular to each other) but how can this be applied to a wavefunction?

Thanks!
 
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In Linear Algebra, abstract vector spaces, we define an inner product that generalizes the dot product of Euclidean spaces. Two vectors are said to be "orthogonal" if and only if their inner product is 0, just as two vectors in R3 are perpendicular if and only if their dot product is 0.

You can show that something like [itex]\int_a^b f(x)\overline{g(x)}dx[/itex] is an "inner product". That is the kind of inner product used when you are talking about "wave functions".
 
Ok.. that helps a bit. Thanks for the explanation :)
 
Orthogonal wavefunctions represent mutually exclusive physical states.

- Warren
 

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