Quantum Mechanics Principles
Physical observables correspond to Hermitian operators:
p̂ = -i ħ d/dx and T̂ = -ħ²/(2m) d²/dx².
The spatial wavepacket ψ(x) transforms via Fourier transform to the momentum distribution φ(p).
Notice how narrowing σₓ spreads the momentum distribution, strictly upholding Heisenberg's bound Δx·Δp ≥ ½ ħ.