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
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.
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
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.