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Direct linkPetersson, T.; Hellsing, B. – European Journal of Physics, 2010
A detailed derivation of analytic solutions is presented for overlap, kinetic, nuclear attraction and electron repulsion integrals involving Cartesian Gaussian-type orbitals. It is demonstrated how s-type orbitals can be used to evaluate integrals with higher angular momentum via the properties of Hermite polynomials and differentiation with…
Descriptors: Mechanics (Physics), Molecular Structure, Computation, Calculus
De Luca, R. – European Journal of Physics, 2012
Observing the way a watering hose is wrapped on a rotating cylinder, a catenary shape is detected for the suspended portion of the hose. We calculate the angle [alpha] the tangent to the curve at the highest point of the suspended portion makes with the horizontal. By means of this quantity, the length of the suspended and dragged portions of the…
Descriptors: Calculus, Mechanics (Physics), Science Instruction, Scientific Concepts
Viana-Gomes, J.; Peres, N. M. R. – European Journal of Physics, 2011
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…
Descriptors: Textbooks, Quantum Mechanics, Calculus, Spreadsheets
Castano, Diego J. – European Journal of Physics, 2011
Although nowadays there are mythbusting teams ready to empirically confirm or deny advertising claims that may seem too good to be true, it is often economically prohibitive to perform the kinds of experiments that are called for. It is therefore sometimes more sensible and efficacious to perform a thought experiment instead, especially if the…
Descriptors: Physics, Motor Vehicles, Calculus, Scientific Concepts
Belendez, Augusto; Alvarez, Mariela L.; Fernandez, Elena; Pascual, Immaculada – European Journal of Physics, 2009
A cubication procedure of the nonlinear differential equation for conservative nonlinear oscillators is analysed and discussed. This scheme is based on the Chebyshev series expansion of the restoring force, and this allows us to approximate the original nonlinear differential equation by a Duffing equation in which the coefficients for the linear…
Descriptors: Calculus, Equations (Mathematics), Computation, Equipment
Dasgupta, Ananda – European Journal of Physics, 2007
The Bondi K-calculus is a delightful method that has been used to provide rich insights into relativistic kinematics. In this paper, we will try to show how several important results of relativistic kinetics can be derived simply by using this approach. In addition, we will also indicate how the K-calculus can be used to simplify certain…
Descriptors: Kinetics, Calculus, Science Instruction, Motion
