The Schrödinger equation is a linear partial differential equation that describes the wave function or state function of a quantum-mechanical system. It is a key result in quantum mechanics, and its discovery was a significant landmark in the development
This is a 12 minute video on the Schrodinger Equation
In this lesson, the Faculty of Khan introduces Quantum Mechanics with a discussion on wavefunctions and the Schrodinger Equation (in 1-D) and how wavefunctions can represent probability density functions (via the norm-squared), and discuss the significance of this representation.
The Faculty of Khan then introduces/revisits some basic Statistics concepts, and end the video with a proof of how the normalization of wavefunctions stays preserved with time.
NOTE: At around 11:30-11:45, I mention how the 'boundary' integrals have to approach zero at +/- infinity. This is true for square-integrable functions that come up in Physics. However, there are exceptions (i.e. square-integrable functions that don't approach zero at infinity). These exceptions aren't found in Physics though, so we'll ignore them, but I figure they're worth mentioning as a footnote.