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## Main Question or Discussion Point

Hello all!

I am at the QM-basics, and now a little bit confused, but maybe someone can easily clarify.

A QM-system can be described by a state that lives in a hilbertspace, this was introduced because superposition is essential. In the solutions of different problems polynomial functions turn up like Laguerre-p., Legendre-pol etc. Do these polynomials live in a vectorspace?

On the other hand alway the term wavefunction is used, which I associate exlusivliy with Cos and Sin-functions. Refers this nomination to the timeevolution part, or is this term more the result of the experimental beginings of qm (doble slit experiment), and superpostion is the only relevant point?

Or is this question nonsense, because it doesn't matter which set of orthonormal functions I choose for my series expansion?

As I said, I am confused, so I'm not sure how to put this question. But maybe you get my point, and can light this up for me.

Thank you!

I am at the QM-basics, and now a little bit confused, but maybe someone can easily clarify.

A QM-system can be described by a state that lives in a hilbertspace, this was introduced because superposition is essential. In the solutions of different problems polynomial functions turn up like Laguerre-p., Legendre-pol etc. Do these polynomials live in a vectorspace?

On the other hand alway the term wavefunction is used, which I associate exlusivliy with Cos and Sin-functions. Refers this nomination to the timeevolution part, or is this term more the result of the experimental beginings of qm (doble slit experiment), and superpostion is the only relevant point?

Or is this question nonsense, because it doesn't matter which set of orthonormal functions I choose for my series expansion?

As I said, I am confused, so I'm not sure how to put this question. But maybe you get my point, and can light this up for me.

Thank you!