Solving Orthonormal Eigenfunctions with Kronecker Delta

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In summary, the conversation is about a person seeking clarification on a question related to QM homework. They have shown that the wavefunction for a particle in an infinite 1D potential well forms an orthonormal set of eigenfunctions and are now asked to express their results in terms of the Kronecker delta. They are confused about what this means, but ultimately realize it is a trivial task.
  • #1
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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  • #2
It's too trivial. Just write <n|m>= \delta_{nm} instead of saying it in words.
 
  • #3
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
 

FAQ: Solving Orthonormal Eigenfunctions with Kronecker Delta

1. What are orthonormal eigenfunctions?

Orthonormal eigenfunctions are a set of functions that satisfy two important properties: orthogonality and normalization. This means that the inner product of any two orthonormal eigenfunctions is equal to 0, and the norm of each function is equal to 1.

2. What is the Kronecker delta?

The Kronecker delta is a mathematical symbol denoted by the Greek letter delta (δ). It is defined as 1 when the two indices are equal, and 0 when they are not equal. In other words, it is a function that takes on the value of 1 only when the inputs are equal, and 0 otherwise.

3. How are orthonormal eigenfunctions solved using the Kronecker delta?

The Kronecker delta is used to simplify the calculation of inner products between orthonormal eigenfunctions. By setting the Kronecker delta equal to 0 when the indices are not equal, the inner product reduces to a single term when the indices are equal. This simplification makes it easier to solve for the eigenvalues and eigenvectors of a system.

4. What are the applications of solving orthonormal eigenfunctions with Kronecker delta?

Orthonormal eigenfunctions and the Kronecker delta are commonly used in fields such as quantum mechanics, signal processing, and linear algebra. They are used to solve problems involving systems that have discrete states or functions, and are also used in the analysis and optimization of complex systems.

5. Are there any limitations to using the Kronecker delta for solving orthonormal eigenfunctions?

The Kronecker delta can only be used for discrete systems, which means that it cannot be applied to continuous functions. Additionally, it may not always be possible to find a complete set of orthonormal eigenfunctions for a given system, which can limit the applicability of this method.

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