Can you think of any analogies of the mathematics of quantum

Can you think of any analogies of the mathematics of quantum mechanics to vectors? What are they, if any? If there are any, would they have any conceptual use?

Solution

Vectors are the essential part of quantum mechanichs. The development of quantum mechanics itself started with the use of vectors. Using the analogy of basis vectors in three dimensions, the idea of hilbert space for infinite dimensional set to satisfy the wavefunction sis developed. Quantum states can be treated as abstract vectors and hence satisfy the principles followed by the vectors.

Conceptually this concept is used in case of spin vectors, then for normalization, finding probability of state and many other cases. It basically forms the the foundations from where the development of the quantum mechanics began and is studied.