7: Matter Waves

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7.1: The Schrödinger Wave Equation
We have a wave equation for light, and light behaves like a particle, so we might expect that the wave equation for particles like electrons would be the same. But it turns out that photons having zero mass and electrons having non-zero mass leads to fundamentally different wave equations for these two entities.
7.2: States of Definite Energy
Our old trick of separation of variables reveals that the time evolution of a quantum state (i.e. how probabilities of measurements change with time) is related to whether the measurement of the energy of that state is a fixed number or is probabilistic.
7.3: Operators and Observables
We have a special set of mathematical tools called operators that allow us to extract information from quantum states. Sometimes these operators give us a single, exact number, and other times they provide us with probabilities for various measurements.
7.4: Eigenstates and Eigenvalues
We use our new operators to do some calculations that predict observable averages and uncertainties.

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