Renormalizing the kinetic energy operator in elementary quantum mechanics

In this paper, we consider solutions to the three-dimensional Schrodinger equation of the form psi(r) = u(r)/r, where u(0) not equal 0. The expectation value of the kinetic energy operator for such wavefunctions diverges. We show that it is possible to introduce a potential energy with an expectation value that also diverges, exactly cancelling the kinetic energy divergence. This renormalization procedure produces a self-adjoint Hamiltonian. We solve some problems with this new Hamiltonian to illustrate its usefulness.

Influence of irradiant energy on degree of conversion, polymerization rate and shrinkage stress in an experimental resin composite system

Objective. This study evaluated the degree of conversion (DC), maximum rate of cure (R(p)(max)), and polymerization stress (PS) developed by an experimental dental composite subjected to different irradiant energies (3,6,12, 24, or 48J/cm(2)) under constant irradiance (500 mw/cm(2)). Methods. DC and R(p)(max) were monitored for 10 min on the bottom surface of 2-mm thick disks and on 150-mu m thick films (representing the top of the specimen) using ATR-FTIR. PS was monitored for 10 min in 2-mm thick disks bonded to two glass rods (O = 5 mm) attached to a universal testing machine. One-way ANOVA/Tukey tests were used and differences in DC and R(p)(max) between top and bottom surfaces were examined using Student`s t-test. Statistical testing was performed at a pre-set alpha of 0.05. Results. For a given surface, DC showed differences among all groups, except at the top between 24 and 48 J/cm(2). R(p)(max) was similar among all groups at the same surface and statistically higher at the top surface. PS also showed significant differences among all groups. Data for 48 J/cm(2) were not obtained due to specimen failure at the glass/composite interface. Significance. Increases in irradiant exposure led to significant increases in DC and PS, but had no effect on R(p)(max) (c) 2008 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved.

Resting energy expenditure of children attending a rehabilitation programme following head injury

Statement of purpose: Increased resting energy expenditure following head injury is well documented, but whether this increase extends into rehabilitation and whether this is affected by changes in body composition have not been studied. The aim of this study was to determine whether children attending a rehabilitation program following head injury had altered energy expenditure and body composition. Methods: Measurements of resting energy expenditure by indirect calorimetry were performed in 21 head injured children (mean age 10.2±3.8 years). Measurement of body composition was performed using total body potassium. Results: Measured resting energy expenditure values were widely distributed, ranging from 52.3-156.4% of predicted values, yet the mean percentage predicted using Schofield weight, Schofield weight and height and World Health Organization predictive equations were 97.5%, 97.4% and 98.6%, respectively. Mean percentage of expected total body potassium for weight, height and age for head injured children were 85.1 ± 15.5%, 89.1 ± 14.1% and 86.9 ± 15.9%, thus all showed significant depletion. Conclusions: During rehabilitation, using predictive equations to estimate resting energy expenditure in this group revealed a small bias on average but very large bias at the individual level. Head injured children had altered resting energy expenditure and body composition.

Energy expenditure during 2nd week of an ultra-endurance run around Australia

Purpose: For ultra-endurance athletes, whose energy expenditure is likely to be at the extremes of human tolerance for sustained periods of time, there is increased concern regarding meeting energy needs. Due to the lack of data outlining the energy requirements of such athletes, it is possible that those participating in ultra-endurance exercise are compromising performance, as well as health, as a result of inadequate nutrition and energy intake. To provide insight into this dilemma, we have presented a case study of a 37-yr-old ultra-marathon runner as he runs around the coast of Australia. Methods: Total energy expenditure was measured over a 2-wk period using the doubly labeled water technique. Results: The average total energy expenditure of the case subject was 6321 kcal.d(-1). Based on the expected accuracy and precision of the doubly labeled water technique the subject's total energy expenditure might range between 6095 and 6550 kcal.d(-1). The subject's average daily water turnover was 6.083 L over the 14-d period and might range between 5.9 L and 6.3 L.d(-1). Conclusions: This information will provide a guide to the energy requirements of ultra-endurance running and enable athletes, nutritionists, and coaches to optimize performance without compromising the health of the participant.

Energy expenditure and the body cell mass in cystic fibrosis

Poor nutritional status in patients with cystic fibrosis (CF) is associated with severe lung disease, and possible causative factors include inadequate intake, malabsorption, and increased energy requirements. Body cell mass (which can be quantified by measurement of total body potassium) provides an ideal standard for measurements of energy expenditure. The aim of this study was to compare resting energy expenditure (REE) in patients with CF with both predicted values and age-matched healthy children and to determine whether REE was related to either nutritional status or pulmonary function. REE was measured by indirect calorimetry and body cell mass by scanning with total body potassium in 30 patients with CF(12 male, mean age = 13.07 +/- 0.55 y) and 18 healthy children (six male, mean age = 12.56 +/- 1.25 y). Nutritional status was expressed as a percentage of predicted total body potassium; Lung function was measured in the CF group by spirometry and expressed as the percentage of predicted forced expiratory volume in 1 s. Mean REE was significantly increased in the patients with CF compared with healthy children (119.3 +/- 3.1% predicted versus 103.6 +/- 5% predicted, P < 0.001) and, using multiple regression techniques, REE for total body potassium was significantly increased in patients with CF (P = 0.0001). There was no relation between REE and nutritional status or pulmonary disease status in the CF group. In conclusion, REE is increased in children and adolescents with CF but is not directly related to nutritional status or pulmonary disease. Nutrition 2001;17:22-25. (C)Elsevier Science Inc. 2001.