Quantum Mechanics in Physics

Once a particle has a wavelength, something has to say how that wavelength behaves, and the Schrodinger equation is that something. It is a wave equation, but its solutions are not numbers you measure. They are wave functions, and squaring one gives the odds of finding the particle in a given place. What makes the equation so productive is that it must be obeyed everywhere at once, including at the walls of whatever container the particle sits in, and only certain energies let the wave fit those edges smoothly. Those energies are the quantum levels, and they were not put in by hand. The blocks give the equation in both forms, the well worked through to its allowed energies, tunneling through a barrier, and the harmonic oscillator, which is the one case that comes up again and again in later physics.