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Tannous, C.; Langlois, J. – European Journal of Physics, 2011
A simple numerical method for the determination of Schrodinger equation eigenvalues is introduced. It is based on a marching process that starts from an arbitrary point, proceeds in two opposite directions simultaneously and stops after a tolerance criterion is met. The method is applied to solving several 1D potential problems including symmetric…
Descriptors: Nuclear Physics, Energy, Physics, Comparative Analysis
Montgomery, H. E., Jr. – European Journal of Physics, 2011
The Schrodinger equation for the ground state of a hydrogen atom confined at the centre of an impenetrable cavity is treated using variational perturbation theory. Energies calculated from variational perturbation theory are comparable in accuracy to the results from a direct numerical solution. The goal of this exercise is to introduce the…
Descriptors: Nuclear Physics, Energy, Science Instruction, College Science
Rapedius, Kevin – European Journal of Physics, 2011
Here, we present complex resonance states (or Siegert states) that describe the tunnelling decay of a trapped quantum particle from an intuitive point of view that naturally leads to the easily applicable Siegert approximation method. This can be used for analytical and numerical calculations of complex resonances of both the linear and nonlinear…
Descriptors: Quantum Mechanics, Equations (Mathematics), Computation, Energy
Ge, Yingbin; Rittenhouse, Robert C.; Buchanan, Jacob C.; Livingston, Benjamin – Journal of Chemical Education, 2014
We have designed an exercise suitable for a lab or project in an undergraduate physical chemistry course that creates a Microsoft Excel spreadsheet to calculate the energy of the S[subscript 0] ground electronic state and the S[subscript 1] and T[subscript 1] excited states of H[subscript 2]. The spreadsheet calculations circumvent the…
Descriptors: Spreadsheets, Equations (Mathematics), Science Instruction, Chemistry
Coutinho, F. A. B.; Amaku, M. – European Journal of Physics, 2009
In this paper, we consider solutions to the three-dimensional Schrodinger equation of the form [psi](r) = u(r)/r, where u(0) [is not equal to] 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…
Descriptors: Quantum Mechanics, Kinetics, Physics, Science Instruction
Peer reviewed
Shore, Bruce W. – American Journal of Physics, 1979
Presents an examination of graphical displays of solutions to time-dependent Schrodinger equation modeling a laser-excited three-level atom. It suggests that an energy level may be regarded as virtual when it is detuned from resonance by more than two Rabi frequencies. (Author/HM)
Descriptors: Atomic Structure, College Science, Energy, Higher Education
Peer reviewed
Ley-Koo, E.; And Others – American Journal of Physics, 1980
Presented are forms of harmonic oscillator attraction and Coulomb wave functions which can be explicitly constructed and which lead to numerical results for the energy eigenvalues and eigenfunctions of the atomic system. The Schrodinger equation and its solution and specific cases of muonic atoms illustrating numerical calculations are included.…
Descriptors: Atomic Structure, College Science, Energy, Higher Education
de Brito, P. E.; Nazareno, H. N. – European Journal of Physics, 2007
In the present work we treat the problem of a particle in a uniform magnetic field along the symmetric gauge, so chosen since the wavefunctions present the required cylindrical symmetry. It is our understanding that by means of this work we can make a contribution to the teaching of the present subject, as well as encourage students to use…
Descriptors: Quantum Mechanics, Measurement Equipment, Probability, Algebra
Peer reviewed
Evans, D. E. – Physics Education, 1980
Describes a general purpose algorithm which enables one to calculate the allowed energy eigenvalues for an arbitrary potential. Results of a calculation where a centrifugal potential is added to the hydrogenic Coulomb potential are discussed. (Author/HM)
Descriptors: Atomic Structure, College Science, Computation, Energy
Solution of the Schrodinger Equation for the Hydrogen Atom using a Modular Analogue Computing System
Peer reviewed
Summers, M. K. – Physics Education, 1975
Descriptors: Atomic Structure, College Science, Computer Assisted Instruction, Energy