Hilbert space

A Hilbert space is a mathematical concept used in quantum mechanics and functional analysis. Think of it as an infinite-dimensional generalization of ordinary space, where instead of just points, we can have functions and more complex structures. It provides a framework for understanding quantum states, allowing for the use of concepts like distance and angles, which help in predicting how systems behave. Essentially, a Hilbert space helps scientists and mathematicians work with and visualize complex problems in physics and other fields, making it easier to understand the underlying principles.