Volume 21: 2008

Peer Reviewed Papers
June 12, 2008
Excited States of the Anharmonic Oscillator Potentials: Variational Method
By Joshua M. Koch, Christopher F. J. Schuck, and Bronson W. Wacker, Department of Physics, University of Nebraska at Omaha
January 10, 2008
Systematic convergence in applying the variational method to anharmonic oscillator potentials
By Thomas L. Johnson III, Elizabeth R. Hegdahl, Andrew R. Ward, and Stanley E. Schnell, Department of Physics, University of Nebraska at Omaha
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June 12, 2008

Excited States of the Anharmonic Oscillator Potentials: Variational Method

By Joshua M. Koch, Christopher F. J. Schuck, and Bronson W. Wacker, Department of Physics, University of Nebraska at Omaha

Abstract

We applied variational method to calculate the first eight eigenvalues of quartic and sextic anharmonic oscillator potentials. By choosing a set of sophisticated trial wave functions, applying the orthogonal conditions between the eigenstates, and with the help of Maple software packages, we found that theses eight eigenvalues accurate and agree well with those obtained from the Runge-Kutta numerical integration method.

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January 10, 2008

Systematic Convergence in Applying the Variational Method to Anharmonic Oscillator Potentials

By Thomas L. Johnson III, Elizabeth R. Hegdahl, Andrew R. Ward, and Stanley E. Schnell, Department of Physics, University of Nebraska at Omaha

Abstract

We applied the variational method to determine the ground and first excited state energies of quartic and sextic anharmonic oscillator potentials.  Starting from two sets of trial wave functions, we showed that by introducing additional terms, the energy eigenvalues gradually converge to those obtained from the Runge-Kutta numerical integration method.

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