An exact problem to be solved is some problem of theoretical physics , the answer for which can be written in the form of elementary or known special functions .
Some precisely solved problems:
- the problem of two bodies interacting with each other only gravitationally , in classical mechanics ;
- problems of a three-dimensional harmonic oscillator , Coulomb potential, uniform magnetic field in quantum mechanics;
- one-dimensional and two-dimensional Ising model in statistical physics .
Some tasks that are not exactly solvable:
- the three-body problem in mechanics and its generalization to several bodies;
- the two-body problem in the general theory of relativity ;
- the helium atom problem (that is, two electrons in the Coulomb potential);
- three-dimensional Ising model.
Literature
- Exact Solutions of Einstein's Equations / Ed. E. Schmutzer. - M .: Energoizdat, 1982. - 416 p.
- Albeverio S., Gestesi F., Hoeg-Kron R., Holden H. Solvable models of quantum mechanics. - M .: Mir, 1991 .-- 568 p.
- Fushchich V.I., Shtellen V.M., Serov N.I. Symmetry analysis and exact solutions of nonlinear equations of mathematical physics. - Kiev: Naukova Dumka, 1989 .-- 334 p.
See also
- Integrable system
- Hamiltonian system
- Theory of Integrable Systems