Position and Momentum

Paul Busch, PEKKA J. LAHTI, Juha-Pekka Pellonpää +1 more

Muhammad Yasin

This article will show you how to measure the position and momentum of a particle simultaneously from the principle of uncertainty .From the principle of position-momentum uncertainty, the position and momentum of a particle can be determined at the same time by fulfilling the condition of uncertainty by multiplying a constant k with the fixed value of position and momentum. Which is known as the principle of certainty.

Mark Burgess

Yuki Senoo, Holger F. Hofmann, Hiroki Yamakami +1 more

The uncertainty principle suggests a quantitative trade-off between the control of position and the control of momentum in particle propagation. However, a superposition of two states with very different uncertainty trade-offs introduces an interference term that seems to combine precise statements about position and about momentum, allowing us to study how quantum mechanics describes the propagation of individual particles in free space. Here, we present a detailed experimental study of photons prepared in a superposition of position and momentum generated in a Sagnac interferometer. The transverse distribution of photons was obtained with three different measurement settings at the output port of the interferometer, corresponding to the initial position distribution, the initial momentum distribution, and an intermediate propagation time at which the contributions of initial position and momentum uncertainties are approximately equal to each other. We show that the interference effect localizes the photons in narrow intervals of position and momentum, resulting in a quantitative violation of Newton's first law as the interference pattern spreads out at the intermediate position. The data obtained can be used to demonstrate the negativity of the Wigner function in regions outside the position and momentum intervals in which the position and momentum contributions are confined.

Muhammad Yasin

This article will show you how to measure the position and momentum of a particle simultaneously from the principle of uncertainty .From the principle of position-momentum uncertainty, the position and momentum of a particle can be determined at the same time by fulfilling the condition of uncertainty by multiplying a constant k with the fixed value of position and momentum. Which is known as the principle of certainty