Physics – Quantum Physics
Scientific paper
2004-12-10
Physics
Quantum Physics
14 pages, 8 figures
Scientific paper
A powerful method for calculating the eigenvalues of a Hamiltonian operator consists of converting the energy eigenvalue equation into a matrix equation by means of an appropriate basis set of functions. The convergence of the method can be greatly improved by means of a variational parameter in the basis functions determined by the principle of minimal sensitivity. In the case of the quartic anharmonic oscillator and of a symmetrical double-well potential we choose an effective oscillator frequency. In the case of nonsymmetrical potential we add a coordinate shift in a two-parameter variational calculation. The method not only gives the spectrum, but also an approximation to the energy eigenfunctions. Consequently it can be used to solve the time-dependent Schr\"odinger equation using the method of stationary states. We apply it to the time development of two different initial wave functions in the double-well slow roll potential.
Amore Paolo
Aranda Alfredo
Fernandez Francisco
Jones Hugh
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