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…

On 24 June 1994 at Fairchild Air Force Base, during practice for an air show, a low-flying B-52H aircraft banked its wings vertically and crashed. Emphasizing the activity of modeling drag and gravity, these notes examine the possibility of recovery with several models. First, with algebra, historical data lead to a model where in a free fall near…

We will present a problem-solving method for the dynamics of a projectile that has two perpendicular acceleration vectors through rotation of the axes. This methodology of reparameterizing the two-dimensional system simplifies the speed optimization calculus.

We present a complete, soup to nuts, modeling activity of a falling column of water. Many colleagues have used this material in teaching applications of first order separable differential equations. We describe how the material can be presented with students collecting their own data from online videos. One can then either offer the differential…

The motion equations of a body under gravity and resistance linearly dependent on speed are usually analysed by solving differential equations. In this paper we report a derivation not explicitly involving differential equations but instead based on some elementary mathematical operations. The derivation uses only knowledge covered in a typical…

The distant magnetic field of a magnetic dipole is usually derived via the magnetic vector potential and substantial vector calculus. This paper presents an alternate proof that is less mathematically intensive, and that ties together various problem-solving tricks (the principle of virtual work, observation that only instantaneous quantities…

In a recent submission to "The Physics Teacher," we related how trigonometric identities can be used to find the extremes of several functions in order to solve some standard physics problems that would usually be considered to require calculus. In this work, the functions to be examined are polynomials, which suggests the utilization of…

Difficulties presented by students on the concept of instantaneous velocity are well known. This is in part due to instantaneous speed being often defined in terms of the notion of mathematical limit, which may not be clear to many students in introductory physics courses. In this work we present a complementary teaching proposal that can help…

One of the memories of my freshman year at Amherst was a lecture in the required physics/calculus course in which Arnold Arons quoted Isaac Newton on standing on the shoulders of giants. Now that I have spent my physics career, I still use the same quote, but now apply it to the eponymous apparatus that has been designed by the giants in our field.

A simple in-class demonstration of integral Calculus for first-time students is described for straightforward whole number area magnitudes, for ease of understanding. Following the Second Fundamental Theorem of the Calculus, macroscopic differences in ordinal values of several integrals, [delta]"F"(x), are compared to the regions of area…

Geometry, calculus and in particular integrals, are too often seen by young students as technical tools with no link to the reality. This fact generates a loss of interest in students with a consequent removal of motivation in the study of such topics and more widely in pursuing scientific curricula. With this note we put to the fore a simple…

The motion of a bead along a path restricted to straight lines (restricted brachistochrone), sliding without friction from rest and accelerated by gravity, is considered. For two shapes of path, the geometry of the route optimized to provide the least travel time from one point to another is obtained. The bead's travel times, path lengths, and…

This paper demonstrates how the transcendental number "e" may be arrived at by observing the discharge of a capacitor through a fixed resistor and then modelling the system using a simple step-wise procedure. The experimental phase makes use of the Arduino microcontroller, while simple modelling of the system is carried out by means of…

This paper is a continuation of an earlier discussion in this journal about adhering to principles of mathematics while presenting function graphs in physics. As in the previous paper, the importance of the vertical line test was examined, this paper delves more in-depth, and it pinpoints a need for presenting graphs with a continuous rate of…

College physics textbooks (algebra based) tend to shy away from topics that are usually thought to require calculus. I suspect that most students are just as happy to avoid these topics. Occasionally, I encounter students who are not so easily satisfied, and have found it useful to maintain a storehouse of non-calculus solutions for some common…