Solving Orthonormal Eigenfunctions with Kronecker Delta

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SUMMARY

The discussion focuses on the concept of orthonormal eigenfunctions in quantum mechanics, specifically in the context of a particle in an infinite one-dimensional potential well. Gareth confirms that he has demonstrated the normalization and orthogonality of the wavefunctions, thus establishing their orthonormality. The Kronecker delta notation, Delta[nm]={1 for n=m and 0 for n!=m}, is clarified as a concise way to express the inner product of these eigenfunctions, represented as = \delta_{nm}.

PREREQUISITES
  • Understanding of quantum mechanics principles, particularly wavefunctions
  • Familiarity with the concept of orthonormality in linear algebra
  • Knowledge of the Kronecker delta function and its applications
  • Basic skills in mathematical notation used in quantum mechanics
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  • Study the properties of eigenfunctions in quantum mechanics
  • Learn about the implications of orthonormal sets in Hilbert spaces
  • Explore the application of the Kronecker delta in various mathematical contexts
  • Review the derivation of wavefunctions for different potential wells
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Students of quantum mechanics, physicists working with wavefunctions, and anyone interested in the mathematical foundations of quantum theory.

ghosts_cloak
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Hello :-)
I am just finishing my QM homework and I have just showed that the wavefunction for a particle in an infinite 1D potential well form an orthonormal set of eigenfunctions. It asks me to express my results in terms of the Kronecker delta:

Delta[nm]={1 for n=m and 0 for n!=m}

Im a bit confused as to what this means... I have shown they are normalised and orthogonal, hence they are orthonormal? I don't see what the last part is asking me to do?

Any help is much appreciated!

~Gareth
 
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It's too trivial. Just write <n|m>= \delta_{nm} instead of saying it in words.
 
Hi, lol!
The question is sooo long I just lost sight of what I was doing. Yep it is trivial, I see now (actually, before I read your post, but thanks a lot anyway)

Cheers,
Gareth
 

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