2004/12/10 by Paolo Amore, Alfredo Aranda, Amore, Paolo +7
Physics and Astronomy · #FOS: Physical sciences #Quantum Physics (quant-ph) #Quantum chaos and dynamical systems #quant-ph
paper · pdf · doi:10.48550/arxiv.quant-ph/0412082
14 pages, 8 figures
arxiv created 2004/12/10 · openalex publication_date 2004/12/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 Schrödinger 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.