Which of the following functions are eigenfunctions of the operation d/dx? Give the eigenvalues where appropriate. (k is a constant)
kx^2, sin kx, (sin kx + cos kx), e^(kx), e^(kx^2), e^(-ikx)
Which of the following functions are eigenfunctions of the operation d/dx? Give the eigenvalues where appropriate....
Please solve the normalization, 7e, and the commutator questions 6. Normalization Normalize the following functions: sin (1") between 0<x<L 200 for 0 <r <o, treating do as a constant 7. Eigenfunctions and Eigenvalues Determine which of the following are eigenfucntions of the operator 4 give the eigenfunction. Where appropriate (a) pikx (b) cos ka (c) k (d) kx (e) e-ax? 8. Commutator Evaluate the commutator (î, P2]
What are the results of operating on the following functions with the operators d/dx and d2/dx2 : a) 4x-3 b) cos(bx), c) eikx d) (x2–i) ? What functions are eigenfunctions of these operators? What are the corresponding eigenvalues?
These functions are eigenfunctions corresponding to the operator d^2/dx^2 What is the eigenvalue corresponding to 1. sin(2pix/a) wave functions
please answer compleltly 2. Find the eigenfunctions and eigenvalues for the differential equation d^2u(x)/dr^2 = -k^2 u(x) in the interval 0 < = x < = a, assuming k is a real number, for the following sets of boundary conditions: (a) bu(0)+cdu/dt|x=0 =0 and bu(a)+cdu/dx|x=a =0 (b) u(0)+a du/dx|x=0 =0 and u(a)-adu/dx|x=a =0 You need not normalize the eigenfunctions. For (b), find the equation which determines the eigenvalues and verify that there is an infinite set of eigenfunctions and eigenvalues;...
Compute the derivative (d/dx) of the following functions a. x3 - 2x b. (x+4)2 c. sin(ωx2) d. 3e-kx
Please explain the solution and write clearly for nu, ber 25. Thanks. 25. Approximate the following functions f(x) as a linear combination of the first four Legendre polynomials over the interval [-1,1]: Lo(x) = 1, Li(x) = x, L2(x) = x2-1. L3(x) = x3-3x/5. (a) f(x) = X4 (b) f(x) = k (c) f(x) =-1: x < 0, = 1: x 0 Example 8. Approximating e by Legendre Polynomials Let us use the first four Legendre polynomials Lo(x) 1, Li(x)...
(1 point) In this problem we find the eigenfunctions and eigenvalues of the differential equation B+ iy=0 with boundary conditions (0) + (0) = 0 W2) = 0 For the general solution of the differential equation in the following cases use A and B for your constants, for example y = A cos(x) + B sin(x)For the variable i type the word lambda, otherwise treat it as you would any other variable. Case 1: 1 = 0 (1a.) Ignoring the...
Which of the following functions are eigenfunctions of the operator B^ if B^=d2f(x)/dx2? Check all that apply. cos(x) e3ix 1−cos(x) x2
Consider the following differential equation. Assume that all eigenvalues are real y" + λy 0, y(0) 0, y(n) + y'(n) 0 (a) Determine the form of the eigenfunctions n(x)-cos μηχ, where u2- O φ n(x)-1-μ tan(A), where-u2-λ 0 φ n(x)-sin μηχ, where μ2-λ O φ n(x)-1-μ cot(A), where-μ2-λ O φη(x) = 1-μ cot(A), where μ = λ Determine the determinantal equation satisfied by the nonzero eigenvalues O μη satisfies cot v/μ -V μ nn satisfies tan v/λπ-- νλ O An...
please solve all 3 Differential Equation problems 3.8.7 Question Help Consider the following eigenvalue problem for which all of its eigenvalues are nonnegative y',thy-0; y(0)-0, y(1) + y'(1)-0 (a) Show that λ =0 is not an eigenvalue (b) Show that the eigenfunctions are the functions {sin α11,o, where αη įs the nth positive root of the equation tan z -z (c) Draw a sketch indicating the roots as the points of intersection of the curves y tan z and y...