Position Uncertainty in the Heisenberg Uncertainty Relation

Position measurements are examined under the assumption that object position x_t and probe position X_t just after the measurement are expressed by a linear combination of positions x_0 and X_0 just before the measurement. The Heisenberg uncertainty relation between the position uncertainty and momentum disturbance holds when the measurement error \epsilon(x_t) for the object position x_t is adopted as the position uncertainty. However, the uncertainty in the measurement result obtained for x_0 is the standard deviation of the measurement result, and not the measurement error \epsilon(x_0). This difference is due to the reduction of a wave packet. The validity of the linearity assumption is examined in detail.Comment: Corrected typos. 18 pages, to be published in Prog. Theor. Phys

Hybridized electronic states in potassium-doped picene probed by soft x-ray spectroscopies

The electronic structure of the unoccupied and occupied states of potassium (K)-doped and undoped picene crystalline films has been investigated by using the element-selective and bulk-sensitive photon-detection methods of X-ray absorption and emission spectroscopies. We observed the formation of the doping-induced unoccupied and occupied electronic states in K-doped picene. By applying the inner-shell resonant-excitation experiments, we observed the evidence for the orbital hybridization between K and picene near the Fermi energy. Furthermore, the resonant X-ray emission experiment suggests the presence of the Raman-active vibronic interaction in K-doped picene. These experimental evidences play a crucial role in the superconductivity of K-doped picene.Comment: 12 pages, 3 figure

Quasi-periodic pulsations in solar hard X-ray and microwave flares

For more than a decade, various studies have pointed out that hard X-ray and microwave time profiles of some solar flares show quasi-periodic fluctuations or pulsations. Nevertheless, it was not until recently that a flare displaying large amplitude quasi-periodic pulsations in X-rays and microwaves was observed with good spectral coverage and with a sufficient time resolution. The event occurred on June 7, 1980, at approximately 0312 UT, and exhibits seven intense pulses with a quasi-periodicity of approximately 8 seconds in microwaves, hard X-rays, and gamma-ray lines. On May 12, 1983, at approximately 0253 UT, another good example of this type of flare was observed both in hard X-rays and in microwaves. Temporal and spectral characteristics of this flare are compared with the event of June 7, 1980. In order to further explore these observational results and theoretical scenarios, a study of nine additional quasi-periodic events were incorporated with the results from the two flares described. Analysis of these events are briefly summarized