Approximating Formulas For The Us

NumericalDifferentiation andIntegration

In later sections, we will derive several formulas like (11.2). Which formula to use for a specific example, and exactly how to use it, will have to be decided in each case. Example 11.3. Let us test the approximation (11.2) for the function f (x) ˘sinx at a ˘ 0.5 (using 64-bit floating-point numbers). In this case we have f 0(x) ˘

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The WKB approximation - Heidelberg University

which will bring us aryv close to the true solution after a large enough n. 1.3 Derivation of WKB We assume that the solution to equation 1 is given by (x) = eiu(x) (9) with u(x) an unknown complex function. Substituting it in 1, we get the following equation of u(x): iu00(x) u0(x)2 + k(x)2 = 0 (10) Now we sovle this ODE with the succesive ...