Common features of set theory and wave functions?

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Hallucinogen
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I would like to know if any of you think there's any sort of connection, analogy, or common features between, sets in set theory and wave functions in QT?

Wave functions lack trajectories, so do sets. Wave functions also distribute over areas, as sets can do. To my understanding, wave functions are also subject to decomposition; for example, an atom has an associated wave function, and this can decompose into the associated wave functions of the particles atoms are believed to be composed of. In exactly the same way, we can view the atom as a set, containing subatomic particles as its elements.

As such sets of objects may correspond to unique superpositions.

I would like to know if I am correct in my analysis and if anyone knows of any explicit common features or properties of mathematical sets and wave functions?
 
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Hallucinogen said:
I would like to know if any of you think there's any sort of connection, analogy, or common features between, sets in set theory and wave functions in QT?
In this lecture at 1:17:20 and forwards (Lecture 1 | Modern Physics: Quantum Mechanics (Stanford)) Leonard Susskind describes the differences between the states in classical mechanics and quantum mechanics. Basically, states in classical mechanics are points in a set (phase space). In quantum mechanics states do not form sets. Instead, states are vectors in vector spaces over the complex numbers.
 
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DennisN said:
In this lecture at 1:17:20 and forwards (Lecture 1 | Modern Physics: Quantum Mechanics (Stanford)) Leonard Susskind describes the differences between the states in classical mechanics and quantum mechanics. Basically, states in classical mechanics are points in a set (phase space). In quantum mechanics states do not form sets. Instead, states are vectors in vector spaces over the complex numbers.

thanks