This video provides a basic introduction to the Schrödinger equation by exploring how it can be used to perform simple quantum mechanical calculations. After explaining the basic structure of the equation, the infinite square well potential is used as a case study. The separation of variables approach is used to solve the Schrödinger equation and Born's probabilistic interpretation of the wavefunction is used to calculate the expectation value of the position of a particle in a box. Stationary states are discussed, and it is shown that a linear superposition of energy eigenstates leads to nonstationary states with uncertain energy. The oscillation frequency of a simple superposition of states is calculated and comparisons with radiation emission from atoms is discussed.

References:
Quantum physics of atoms, molecules, solids, nuclei and particles Eisberg and Resnick (Motivating the structure of the Schrodinger equation)
Introduction to Quantum Mechanics Griffiths and Schroeter (Examples of expectation values and superposition of states).
Introduction to Quantum Mechanics Phillips
Vibrations and Waves King
The Quantum Story Jim Baggot
Quantum Physics for Dummies Steven Holzner
Thirty Years that Shook Physics Gamow
Inward Bound Abraham Pais

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https://iopscience.iop.org/article/10...
https://iopscience.iop.org/article/10...