HW3 - ( 29 ( 29 ' u dx du u u = = . 1. Write a program to...

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PHYSICS 4605 Wave Mechanics II Spring 2001 Homework #3 (graded) Due Feb. 5, 2001 Read and absorb Liboff 7.2, 7.9, 7.10, 11.14, 8.2, 8.3, 8.4 Part I: Textbook problems Do problems in Liboff 7.16, 7.63, 7.64, 7.67, 7.68 Part II: Numerical problem (to be used in Project #1) For the 1D S.E., we can use the formulation: ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 - = = n n n n n E r V m x F x u x F x u 2 2 , H where u(x) is the space-dependent part of the wavefunction. For this assignment, solve the second order differential equation numerically as a mathematical exercise, using the Euler method, which is ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 x x u x F x u x u x x u x u x u i i i i i i i + = + = + + 1 1 , where you must define the intial conditions,
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Unformatted text preview: ( 29 ( 29 ' u dx du u u = = . 1. Write a program to solve the D.E. Use a function subroutine to generate F(x). 2. Solve the differential equation exactly for the cases F(x)=1 and F(x)=-1. Then use your program to solve the DE numerically for these cases. 3. Calculate the error of your numerical result, u num , compared to the exact result, u ex , as a function of the step size x. Do this by plotting an error function, ,as a function of x. Be sure to use the same overall range of x as you change x. ( 29 =-= N i ex i num i u u N 1 2 1...
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