What are the results of operating on the following functions with the operators d/dx and d2/dx2...
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?
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What are the results of operating on the following functions
with the operators d/dx and d2/dx2...
1. Consider the following operators: a. T = ve dax2 b. p = Wild c. 8=...
1. Consider the following operators: a. T = ve dax2 b. p = Wild c. 8= x Are the following functions (i.-iv. eigenfunctions of operators a, b, or c? If so, provide the eigenvalue. i. 4 cos (4x) ii. e-7x iii. ei3x iv. x2-3
Which of the following functions are eigenfunctions of the operator B^ if B^=d2f(x)/dx2? Check all that...
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
2. Evaluate a. [sin z,d/dz] b. [d2/dx,ax2 + bx + c] where a, b, and c...
2. Evaluate a. [sin z,d/dz] b. [d2/dx,ax2 + bx + c] where a, b, and c are const. c. [d/dx , da/dx2]
Which of the following functions are eigenfunctions of the operation d/dx? Give the eigenvalues where appropriate....
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)
These functions are eigenfunctions corresponding to the operator d^2/dx^2 What is the eigenvalue corresponding to 1....
These functions are eigenfunctions corresponding to the operator d^2/dx^2 What is the eigenvalue corresponding to 1. sin(2pix/a) wave functions
Consider the finite difference matrix operator for the 1D model problem u(/d2- f(x) on domain [0,...
Consider the finite difference matrix operator for the 1D model problem u(/d2- f(x) on domain [0, 1] with boundary conditions u(0) = 0 and u(1) = 0, given by [-2 1 1-2 1 E RnXn h2 1 -2 1 This matrix can be considered a discrete version of the continuous operator d/da2 that acts upon a function(r). (a) Show that the n eigenvectors of A are given by the vectors ) (p-1,... , n) with components and with eigenvalues h2...
Which of the following statements is incorrect. Select one: O a. Hermition operators do not give...
Which of the following statements is incorrect. Select one: O a. Hermition operators do not give real eigenvalues O b. Eigenfunctions must go to zero as X goes to infinity O c. The Hamiltonian is a Hermitian operator O d. eigenfunctions of Hermitian operators with different eigenvalues are orthogonal e. As temperature increases, the wavelength corresponds to the maximum intensity in black body radiation shifts to lower wavelength For a particle in a box of length L and in state...
Q1 dx, 115 5xita dx. 2) ſ tan°4x dx . 3) 06-341 S[cos(x? 4) + 1)...
Q1 dx, 115 5xita dx. 2) ſ tan°4x dx . 3) 06-341 S[cos(x? 4) + 1) + xdx, 5) prove that I cscu du = -Inlcscu + cotul + c x2 + Q2 r3 dx 1) dx 2) sino cosºede , 3) /* sec°8 de , 4) * sec`e do , 4) , Port + 4 1 5) dx . 4- x2) 4 Q3 Answer A or B (graph the functions) A-Determine the area of the region enclosed by y...
explain please 2. Which one of the following DE is exact? a. (x+y)dx+(xy+1) dy=0 b (e...
explain please
2. Which one of the following DE is exact? a. (x+y)dx+(xy+1) dy=0 b (e + y)<x+ſe+x)dy = 0 c.(ye* +1) dx +(e' + xy) dy = 0 d. (sin x+cos y) dx +(cos x +sin y) dy = 0 e. (eº+1) dx +(e? + 2) dy = 0 3. The solution of the following separable DE xy' =-y? is a. y= '+c b. y=- c. y = In x+c In x+c d. In y=x? + e. yer+C 4....
Linearity is an important concept to be familiar with. For the following operators, L.), determine if...
Linearity is an important concept to be familiar with. For the following operators, L.), determine if they are linear or nonlinear a. L (x) = ax2 + bx b. L (x) = Vax C. L = m + ad, so that L(f)= *+af d. L (f) = $x f(x)dx
1. Consider the following operators: a. T = ve dax2 b. p = Wild c. 8= x Are the following functions (i.-iv. eigenfunctions of operators a, b, or c? If so, provide the eigenvalue. i. 4 cos (4x) ii. e-7x iii. ei3x iv. x2-3
2. Evaluate a. [sin z,d/dz] b. [d2/dx,ax2 + bx + c] where a, b, and c are const. c. [d/dx , da/dx2]
Consider the finite difference matrix operator for the 1D model problem u(/d2- f(x) on domain [0, 1] with boundary conditions u(0) = 0 and u(1) = 0, given by [-2 1 1-2 1 E RnXn h2 1 -2 1 This matrix can be considered a discrete version of the continuous operator d/da2 that acts upon a function(r). (a) Show that the n eigenvectors of A are given by the vectors ) (p-1,... , n) with components and with eigenvalues h2...
Which of the following statements is incorrect. Select one: O a. Hermition operators do not give real eigenvalues O b. Eigenfunctions must go to zero as X goes to infinity O c. The Hamiltonian is a Hermitian operator O d. eigenfunctions of Hermitian operators with different eigenvalues are orthogonal e. As temperature increases, the wavelength corresponds to the maximum intensity in black body radiation shifts to lower wavelength For a particle in a box of length L and in state...
Q1 dx, 115 5xita dx. 2) ſ tan°4x dx . 3) 06-341 S[cos(x? 4) + 1) + xdx, 5) prove that I cscu du = -Inlcscu + cotul + c x2 + Q2 r3 dx 1) dx 2) sino cosºede , 3) /* sec°8 de , 4) * sec`e do , 4) , Port + 4 1 5) dx . 4- x2) 4 Q3 Answer A or B (graph the functions) A-Determine the area of the region enclosed by y...
explain please
2. Which one of the following DE is exact? a. (x+y)dx+(xy+1) dy=0 b (e + y)<x+ſe+x)dy = 0 c.(ye* +1) dx +(e' + xy) dy = 0 d. (sin x+cos y) dx +(cos x +sin y) dy = 0 e. (eº+1) dx +(e? + 2) dy = 0 3. The solution of the following separable DE xy' =-y? is a. y= '+c b. y=- c. y = In x+c In x+c d. In y=x? + e. yer+C 4....
Linearity is an important concept to be familiar with. For the following operators, L.), determine if they are linear or nonlinear a. L (x) = ax2 + bx b. L (x) = Vax C. L = m + ad, so that L(f)= *+af d. L (f) = $x f(x)dx
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