Editing Quantum Mechanics (section)

== <span style="color: #FFFFFF;">Understanding</span> ==
Quantum mechanics shifted the paradigm of physics from determinism to probability. In the "Copenhagen interpretation," a particle does not have a definite position until it is observed. Instead, it exists as a "cloud" of probabilities defined by the wave function.

'''The Uncertainty Principle''': Werner Heisenberg showed that the act of measuring a particle's position disturbs its momentum, and vice-versa. Mathematically, ΔxΔp ≥ ħ/2. This is not a limit of our technology, but a fundamental property of the universe. It implies that at the smallest scales, the world is inherently fuzzy.

'''Entanglement and Non-locality''': When two particles are entangled, measuring the spin of one instantaneously determines the spin of the other, regardless of the distance between them. Einstein famously called this "spooky action at a distance." It has been experimentally proven (Bell test experiments) and forms the basis for quantum teleportation and quantum cryptography.

'''The Schrödinger Equation''': This equation describes how the wave function of a physical system changes over time. It is a linear partial differential equation. Solving it for the hydrogen atom explains the discrete energy levels of electrons, which in turn explains the structure of the periodic table and the nature of chemical bonds.
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