Short answers, pulled from the story.
A single electron in a hydrogen atom exists as a cloud of probability rather than a fixed point. The brighter areas on the wave function diagram represent a higher chance of finding that particle at a specific location.
Modern quantum mechanics was born in the mid-1920s when Werner Heisenberg, Max Born, and Pascual Jordan developed matrix mechanics in 1925. Erwin Schrödinger invented wave mechanics during this same period before Born introduced the probabilistic interpretation of his wave function in July 1926.
Predictions made by quantum electrodynamics agree with experimental results regarding the magnetic properties of an electron to within one part in 10^12. This extremely high degree of accuracy demonstrates that quantum mechanics holds true even for complex molecules containing thousands of atoms.
Quantum tunneling allows a particle to cross a potential barrier even if its kinetic energy is smaller than the maximum of that potential. This phenomenon enables radioactive decay and nuclear fusion within stars by allowing particles to pass through barriers they could not overcome classically.
Important applications include quantum chemistry, quantum optics, and quantum computing systems. Superconducting magnets, light-emitting diodes, transistors, semiconductors, magnetic resonance imaging machines, and scanning tunneling microscopes all utilize quantum rules to control electron flow or image surfaces at the atomic level.