The Quantum Revolution: Waves, Uncertainty, and Probability

Explain de Broglie's hypothesis as a symmetry argument: if light has particle properties, matter should have wave properties.

Articulate how the standing wave condition for an electron in an atom naturally leads to quantized energy levels, resolving Bohr's arbitrary postulate.

State the Heisenberg Uncertainty Principle and explain its origin as a fundamental property of wave-like systems, not a limitation of measurement.

Interpret the wave function (Ψ) as encoding the probability amplitude of a particle's location, marking the shift from deterministic trajectories to probabilistic clouds.

Describe qualitatively what the Schrödinger equation represents and why its solutions (eigenstates) correspond to the allowed, stable energy states of an atom.