Schrödinger group

The Schrödinger group is a set of mathematical transformations that preserve the form of the Schrödinger equation, which describes quantum particles like electrons. Think of it as the symmetry rules that allow us to change a quantum system’s description—such as shifting its position, timing, or scale—without affecting its fundamental behavior. These transformations help physicists understand how quantum systems behave under different conditions, ensuring the laws of quantum mechanics stay consistent when we observe or manipulate systems in various ways. Essentially, the Schrödinger group maps solutions of the Schrödinger equation into other valid solutions, highlighting underlying symmetries.