Quantum Chemistry || Lec # 6 || Heisenberg Uncertainty Principle || Dr Rizwana

Heisenberg’s uncertainty principle sets a hard limit on how precisely certain pairs of properties of a particle can be known at the same time—most famously, position and momentum. Because matter behaves like both a wave and a particle, it becomes impossible to measure two “conjugate” properties with perfect accuracy simultaneously. The key consequence is a trade-off: tightening the measurement of one property inevitably loosens the certainty of the other.

In the lecture’s framing, the principle is presented as a statement about position (Δx) and momentum (Δp). The product of their uncertainties must be greater than or equal to a constant involving Planck’s constant (h), often written in the form Δx·Δp ≥ h/2. That relationship captures the inverse behavior: if the uncertainty in position is reduced, the uncertainty in momentum must increase, and vice versa. The lecture also emphasizes what “conjugate properties” means here—properties that are linked so that uncertainty in one automatically introduces uncertainty in the other.

A concrete example centers on an electron orbiting the nucleus. If the goal is to determine the electron’s exact position within a specific atomic orbital, the measurement cannot be perfectly noninvasive. The lecture explains why: locating such a tiny object requires extremely fine instrumentation, and in practice that means using very small-scale probes—described as a “super microscope” that uses photons (light particles) to interact with the electron.

When photons strike the electron, the resulting light helps pinpoint where the electron is. But the same interaction disturbs the electron’s momentum. After the photon collision, the electron’s velocity increases because momentum changes, and since momentum is tied to motion through the relation momentum = mass × velocity (with mass treated as constant), any disturbance in momentum corresponds to a disturbance in velocity. That disturbance is precisely what creates the uncertainty in momentum that the uncertainty principle predicts.

The lecture then narrows the principle’s relevance to microscopic particles—electrons, protons, and neutrons—whose sizes are far beyond what the naked eye can resolve. For these small scales, the measurement process itself is inseparable from the physical quantities being measured. In the atomic context, the uncertainty principle is used to connect measurement limits to the structure of the atomic model: the electron’s position cannot be pinned down with absolute precision, and the resulting momentum uncertainty is an unavoidable part of describing its behavior.

Overall, the uncertainty principle is portrayed as both a theoretical constraint and a practical measurement limitation. It explains why atomic-scale “orbits” cannot be treated like deterministic paths with exact positions at every instant, and why any attempt to localize an electron sharply will necessarily introduce uncertainty in its momentum—shaping how quantum chemistry and quantum physics describe matter at the smallest scales.