Quantum Mechanics
Essential formulas and concepts in quantum mechanics
Planck-Einstein Relation
\(E = h\,f\)
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Indicates that electromagnetic radiation is quantized into photons, each with energy proportional to frequency. Higher frequency (e.g., X-rays) means higher energy per photon than lower frequency (e.g., radio waves).
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de Broglie Wavelength
\(\displaystyle \lambda = \frac{h}{p}\)
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Schrödinger’s Equation (Time-Independent)
\(-\frac{\hbar^2}{2m}\nabla^2 \psi + V \psi = E \psi\)
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Heisenberg Uncertainty Principle
\(\displaystyle \Delta x\,\Delta p \ge \frac{\hbar}{2}\)
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There’s a fundamental limit to how precisely we can simultaneously know certain pairs of observables (like position and momentum). This is not due to measurement flaws, but inherent to quantum systems.
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Photoelectric Effect (Energy Conservation)
\(K_{\text{max}} = h f - \phi\)
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