Does ΔPΔX = ΔEΔT? From the Uncertainty Principle we know that ΔPΔX ≥ hbar/2 and ΔEΔT ≥ hbar/2. I know it is an inequality and not an identity. However, when I do the math it appears to me that ΔPΔX = ΔEΔT. Taking the limits it appears to me that it leads to the differential equation dP/dt = dE/dx, or in other words, the time derivative of momentum equals the space derivative of energy, which I think is correct.