ABSTRACT
WKBJ theory is a method of finding the global behavior of the solution to a linear differential equation for which the highest derivative is multiplied by a small parameter . In a sense, boundary layer theory can be considered as a special case of WKBJ theory, although boundary layer theory can apply to non-linear equations, whereas WKBJ theory cannot. The acronym stands for the main mathematicians that developed the theory, Gregor Wentzel, Henrik Kramers, Marcel Louis Brillouin, and Sir Harold Jeffreys. The latter actually developed the theory three years earlier, in 1923, as a general method for approximating the solutions to linear second order equations, including the Schro¨dinger equation. In spite of his precedence, Jeffreys contribution is often ignored by many sources, so the theory is sometimes referred to as WKB theory. Actually, there are many mathematicians that preceded all four of these mathematicians, including Francesco Carlini (1817), Joseph Liouville (1837), George Green (1837), Lord Rayleigh (1912) and Richard Gans (1915).
