Erwin Schrödinger, an Austrian physicist, developed the Schrödinger equation as part of his efforts to explain the behavior of quantum particles, particularly electrons. The Schrödinger equation is a fundamental equation in quantum mechanics that describes the wave-like behavior of quantum systems.
At the time Schrödinger was working, there was a well-known experimental phenomenon called Young's double-slit experiment. In this experiment, a beam of light or a stream of particles (such as electrons) is directed at a barrier with two closely spaced slits. The particles passing through the slits create an interference pattern on a screen placed behind the barrier, indicating that they exhibit wave-like properties.
Schrödinger wanted to provide a mathematical framework that could describe the behavior of particles as both particles and waves, as observed in the double-slit experiment. He aimed to develop an equation that would yield a wave function, a mathematical description of the particle's behavior, which could be used to determine the probability of finding the particle in different locations.
By formulating the Schrödinger equation, Schrödinger introduced the concept of wave functions in quantum mechanics. The equation describes how the wave function evolves over time and how it relates to the energy of the system. Solving the Schrödinger equation allows one to obtain the wave function and make predictions about the behavior of quantum particles, including the probabilities of various outcomes when measurements are made.
The Schrödinger equation successfully explained the interference pattern observed in Young's double-slit experiment by treating particles as waves described by their respective wave functions. It laid the foundation for understanding the wave-particle duality of quantum particles and became a cornerstone of quantum mechanics.