In theoretical physics, the eikonal approximation (Greek εἰκών for likeness, icon or image) is an approximative method useful in wave scattering equations which occur in optics, quantum mechanics, quantum electrodynamics, and partial wave expansion.
The main advantage the eikonal approximation offers is that the equations reduce to a differential equation in a single variable. This reduction into a single variable is the result of the straight line approximation or the eikonal approximation which allows us to choose the straight line as a special direction.
Relation to the WKB approximation
The early steps involved in the eikonal approximation in quantum mechanics are very closely related to the WKB approximation. It, like the eikonal approximation, reduces the equations into a differential equation in a single variable. But the difficulty with the WKB approximation is that this variable is described by the trajectory of the particle which, in general, is complicated.
Making use of WKB approximation we can write the wave function of the scattered system in term of action S:
We write S as a ħ power series
For the zero-th order:
If we consider the one-dimensional case then .
for V → 0, z → -∞.
- Eikonal Approximation K. V. Shajesh Department of Physics and Astronomy, University of Oklahoma
- R.R. Dubey (1995). Comparison of exact solution with Eikonal approximation for elastic heavy ion scattering (3rd ed.). NASA.
- W. Qian, H. Narumi, N. Daigaku. P. Kenkyūjo (1989). Eikonal approximation in partial wave version (3rd ed.). Nagoya.
- M. Lévy, J. Sucher (1969). "Eikonal Approximation in Quantum Field Theory". Phys. Rev (Maryland, USA). doi:10.1103/PhysRev.186.1656.
- I. T. Todorov (1970). "Quasipotential Equation Corresponding to the Relativistic Eikonal Approximation". Phys. Rev D (New Jersey, USA). doi:10.1103/PhysRevD.3.2351.
- D.R. Harrington (1969). "Multiple Scattering, the Glauber Approximation, and the Off-Shell Eikonal Approximation". Phys. Rev (New Jersey, USA). doi:10.1103/PhysRev.184.1745.
|This applied mathematics-related article is a stub. You can help Wikipedia by expanding it.|
|This quantum mechanics-related article is a stub. You can help Wikipedia by expanding it.|