Adults and children easily distinguish between fine-grained variations in trustworthiness intensity based on facial appearance, but the developmental origins of this fundamental social skill are still debated. Using a fast periodic visual stimulation (FPVS) oddball paradigm coupled with electroencephalographic (EEG) recording, we investigated…

At an early stage of learning quantum chemistry, undergraduate students usually encounter the concepts of the particle in a box, the harmonic oscillator, and then the particle on a sphere. Rotational levels of a diatomic molecule can be well approximated by the energy levels of the particle on a sphere. Wave functions for the particle in a…

Seventy-two junior high general music students were taught to identify primary harmonic functions by using either a scalar or root harmonic aural perception technique. Students were then tested with an aural identification battery. The scalar technique appeared to be the more effective procedure for teaching primary harmonic functions. (Author/SJL)

We derive the energy levels associated with the even-parity wavefunctions of the harmonic oscillator with an additional delta-function potential at the origin. Our results bring to the attention of students a non-trivial and analytical example of a modification of the usual harmonic oscillator potential, with emphasis on the modification of the…

An alternative method for obtaining analytical solutions of the time-independent Schrödinger equation (TISE) is developed and applied to 1-dimensional model quantum systems of interest in atomic and molecular physics. The method is based on proposing a wave function that is a product of two functions, one of them an integrating factor. The…

An individual harmonic wave (i.e., having a single frequency and wavelength over all time and space) traveling in a loss-free medium has a single constant speed, which is equal to the magnitude of the phase velocity of the wave. However, when a set of different harmonic waves are traveling in the same direction, they interfere to form wave…

The purpose of this research was to examine the effect of harmonic accompaniment on the tonal achievement and tonal improvisations of young children. The specific problems of this study were the following: (1) Does the addition of a root melody accompaniment to song instruction affect the tonal achievement of children in kindergarten and first…

A general result for the integrals of the Gaussian function over the harmonic oscillator wavefunctions is derived using generating functions. Using this result, an example problem of a harmonic oscillator with various Gaussian perturbations is explored in order to compare the results of precise numerical solution, the variational method, and…

The real-time graphing of simple harmonic motion of mass on springs with an Arduino based on an experiment set for teaching and learning physics in high schools where students can learn from real experiences. The objectives of this study are to create and develop a real-time measurement for vertical oscillations of mass on springs using the…

The purpose of this study was to determine the effectiveness of sight-singing instruction using specific pitch skills emphasizing scale degree and harmonic function. Fifteen pitch skills encompassing scalar, cadential, and chordal tasks were included in the study. Over a 12-week period, two randomly assigned groups of novice high school singers…

In applying the variational method, six different sets of trial wave functions are used to calculate the ground state and first excited state energies of the strongly bound potentials, i.e. V(x)=x[2m], where m = 4, 5 and 6. It is shown that accurate results can be obtained from thorough analysis of the asymptotic behaviour of the solutions.…

A 36-year-old female with severe spastic dysarthria participated in this study. She received 4 weeks of individual, intensive voice-focused treatment. Voice recordings were conducted at three baseline points, immediately posttreatment, and at a 4-month follow-up. The primary outcome variables were selected acoustic measures of vocal function:…

In two-level designs, the total sample is a function of both the number of Level 2 clusters and the average number of Level 1 units per cluster. Traditional multilevel power calculations rely on either the arithmetic average or the harmonic mean when estimating the average number of Level 1 units across clusters of unbalanced size. The current…

An elementary method based on classical Green's functions for the calculation of the momentum autocorrelation function for a harmonic oscillator and a damped harmonic oscillator is presented. (BB)

The oscillations of one mass "m" suspended between two different springs, assuming a friction force proportional to the velocity [minuscule], have been studied. For this purpose, an assembly for this system has been made. The movement of the mass is recorded with a smartphone and analysed with "Tracker." It is obtained that the…