Probability: The Heisenberg Uncertainty Principle

OpenStaxCollege

Dewi Wulandari

Most physics books do not reveal clearly how the Heisenberg uncertainty principle was derived. This uncertainty comes from the consequence of the wave-particle duality of matter giving statement that position and momentum cannot be measured in the same time. This article tries to reveal mathematics background behind the expression the Heisenberg uncertainty using supported mathematics background such as Fourier transform, Fourier transform integral, the probability of Gaussian distribution and it ends up with the expression of wave function which describe the localized particle giving relation Heisenberg uncertainty principle.

Charles H. Holbrow, James N. Lloyd, Joseph C. Amato

Nana Cabo Bizet, Octavio Obregón, Wilfredo Yupanqui

The Heisenberg uncertainty principle is known to be connected to the entropic uncertainty principle. This correspondence is obtained employing a Gaussian probability distribution for wave functions associated to the Shannon entropy. Independently, due to quantum gravity effects the Heisenberg uncertainty principle has been extended to a Generalized Uncertainty Principle (GUP). In this work, we show that GUP has been derived from considering non-extensive entropies, proposed by one of us. We found that the deformation parameters associated with S+ and S− entropies are negative and positive respectively. This allows us to explore various possibilities in the search of physical implications. We conclude that non-extensive statistics constitutes a signature of quantum gravity.

Charles H. Holbrow, James N. Lloyd, Joseph C. Amato +2 more

F. J. Duarte

Heisenberg’s uncertainty principle, Δ p Δ x ≈ h , is derived from the generalized quantum N -slit interferometric probability. Various versions of the uncertainty principle utilized in quantum optics are introduced in the chapter. Applications to beam divergence Δθ, astronomical telescopes, and the tuning of laser microcavities are discussed.