| Journal: | Brazilian journal of physics |
| Database: | PERIÓDICA |
| System number: | 000408756 |
| ISSN: | 0103-9733 |
| Authors: | Santos, R.C1 Santos, J1 Lima, J.A.S2 |
| Institutions: | 1Universidade Federal do Rio Grande do Norte, Departamento de Fisica, Natal, Rio Grande do Norte. Brasil 2Universidade de Sao Paulo, Instituto de Astronomia, Geofisica e Ciencias Atmosfericas, Sao Paulo. Brasil |
| Year: | 2006 |
| Season: | Dic |
| Volumen: | 36 |
| Number: | 4A |
| Pages: | 1257-1261 |
| Country: | Brasil |
| Language: | Inglés |
| Document type: | Artículo |
| Approach: | Experimental, analítico |
| English abstract | The classical and relativistic Hamilton-Jacobi approach is applied to the one-dimensional homogeneous potential, V(q) = αqn, where α and n are continuously varying parameters. In the non-relativistic case, the exact analytical solution is determined in terms of α, n and the total energy E. It is also shown that the non-linear equation of motion can be linearized by constructing a hypergeometric differential equation for the inverse problem t(q). A variable transformation reducing the general problem to that one of a particle subjected to a linear force is also established. For any value of n, it leads to a simple harmonic oscillator if E > 0, an “anti-oscillator” if E < 0, or a free particle if E = 0. However, such a reduction is not possible in the relativistic case. For a bounded relativistic motion, the first order correction to the period is determined for any value of n. For n >> 1, it is found that the correction is just twice that one deduced for the simple harmonic oscillator (n = 2), and does not depend on the specific value of n |
| Disciplines: | Física y astronomía |
| Keyword: | Física, Física de partículas y campos cuánticos, Relatividad, Ecuación de Hamilton-Jacobi, Mecánica clásica |
| Keyword: | Physics and astronomy, Particle physics and quantum fields, Physics, Relativity, Hamilton-Jacobi equation, Classical mechanics |
| Full text: | Texto completo (Ver PDF) |
