Common features of set theory and wave functions?

In summary, there are some notable similarities between sets in set theory and wave functions in quantum mechanics. Both lack trajectories and can be subject to decomposition. Additionally, sets and wave functions can correspond to unique superpositions. However, there are also significant differences, such as states in quantum mechanics being vectors in vector spaces rather than points in sets like in classical mechanics.
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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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The only common feature is that you can define any function by sets. I think your comparison is too far-fetched to make any sense.
 
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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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A vector space is a set of elements together with a field (like the real or complex numbers) called vectors with some algebraic operations defined on these sets. Today nearly everything in math is based on set theory.
 
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  • #5
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
 

FAQ: Common features of set theory and wave functions?

What is set theory and how is it related to wave functions?

Set theory is a branch of mathematics that deals with the study of sets, which are collections of objects. It is closely related to wave functions in quantum mechanics, as sets can be used to represent the possible states of a system, and wave functions describe the probability amplitudes for a particle to be in a particular state.

What are some common features between set theory and wave functions?

Both set theory and wave functions use mathematical notation to represent the elements or states of a system. They also both involve the concept of superposition, where multiple states can exist simultaneously. Additionally, both are used to make predictions about the behavior of a system.

How do set theory and wave functions differ?

While both set theory and wave functions deal with the concept of states, they approach it from different perspectives. Set theory focuses on the collection of all possible states, while wave functions describe the probability of a particle being in a specific state. Additionally, set theory is a purely mathematical concept, while wave functions have physical interpretations in quantum mechanics.

Can set theory be used to describe wave functions in classical mechanics?

No, set theory is primarily used in the context of quantum mechanics, where the behavior of particles is described by wave functions. Classical mechanics, on the other hand, uses different mathematical concepts and equations to describe the motion of macroscopic objects.

How are set theory and wave functions used in practical applications?

Set theory is used in various fields of mathematics, such as topology and algebra, to study abstract structures and relationships between objects. Wave functions, on the other hand, have practical applications in quantum computing, cryptography, and other areas of quantum technology.

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