Harmonic analysis approach to the proof of Heisenberg inequality

the Heisenberg uncertainty Principle is a fundamental principle in quantum mechanics, which was developed by the German physicist Werner Heisenberg and was proposed by him in 1927. This principle states that for a pair of physical quantities that share phase space, such as position and momentum, it is impossible to accurately measure their values at the same time. There are several variants of it in harmonic analysis studies, and the article will introduce some of them in R¹ space and L² space. In the process of providing the Heisenberg inequality, the article proved the Plancherel identity and Schwartz inequality by using Fourier transform and inverse Fourier transform. Finally, author solved the equation of the wave function (x). The famous physicists Heisenberg proposed one of the more novel ideas in quantum mechanics the existence of unobservable orbits cannot be assumed, which did bring great influence in quantum mechanics. The article will introduce the conception of Heisenberg inequality and try to finish the proof.