Uncertainty Principle -- from Eric Weisstein's World of Physics (original) (raw)

A quantum mechanical principle due to Werner Heisenberg Eric Weisstein's World of Biography (1927) that, in its most common form, states that it is not possible to simultaneously determine the position and momentum of a particle. Moreover, the better position is known, the less well the momentum is known (and vice versa). The principle is sometimes known as the Heisenberg uncertainty principle, and can be stated exactly as

	(1)

where is the uncertainty in position, is the uncertainty in momentum, and ish-bar (Landau and Lifschitz 1977, p. 48; Gasiorowicz 1995, p. 120). Care is necessary since versions of this equation using Planck's constant h instead of , omitting the factor of 2 (Cassidy 1991, p. 234), or both (Pais 1991, p. 305) are commonly found in the literature. Heisenberg's original paper does not attempt to rigorously determine the exact quantity on the right side of the inequality, but rather uses physical argument to show that the uncertainty between conjugate quantum mechanical variables is approximately h (Heisenberg 1927, p. 175, eqn. 1).

References

Cassidy, D. "Certain of Uncertainty." Ch. 12 in Uncertainty: The Life and Science of Werner Heisenberg. New York: W. H. Freeman, pp. 226-246, 1991.

Cassidy, D. C. "Answer to the Question: When Did the Indeterminacy Principle Become the Uncertainty Principle?" Amer. J. Phys. 66, 278-279, 1998.

Gasiorowicz, S. Quantum Physics, 2nd ed. New York: Wiley, 1995.

Heisenberg, W. "Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik." Z. für Phys. 43, 172-198, 1927.

Landau, L.D. and Lifschitz, E. M. Quantum Mechanics (Non-Relativistic Theory), 3rd ed. Oxford, England: Pergamon Press, 1977.

Pais, A. "The Uncertainty Relations, with a Look Back at the Correspondence Principle." §14(d) in Niels Bohr's Times: In Physics, Philosophy, and Polity. Oxford, England: Oxford University Press, pp. 304-309, 1991.