A non-perturbative method for time-dependent problems in quantum mechanics
| dc.creator | Amore, Paolo | |
| dc.creator | Aranda, Alfredo | |
| dc.creator | Fernandez, Francisco | |
| dc.creator | Jones, Hugh | |
| dc.date | 2004-12-10 | |
| dc.date.accessioned | 2026-07-07T06:11:45Z | |
| dc.date.available | 2026-07-07T06:11:45Z | |
| dc.description | 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. | |
| dc.description | 14 pages, 8 figures | |
| dc.identifier | https://arxiv.org/abs/quant-ph/0412082 | |
| dc.identifier | http://arxiv.org/abs/quant-ph/0412082 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/92578 | |
| dc.subject | Quantum Physics | |
| dc.title | A non-perturbative method for time-dependent problems in quantum mechanics | |
| dc.type | text |