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
Which of the following functions are eigenfunctions of the operator B^ if B^=d2f(x)/dx2? Check all that...
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?
A set of functions Ψη are found to be eigenfunctions of operator A with eigenvalues an, and simultaneously also eigenfunctions of operator B with eigenvalue bn. Show that this means that the two operators commute, i.e. A、B-0, at least with respect to these functions.
These functions are eigenfunctions corresponding to the operator d^2/dx^2 What is the eigenvalue corresponding to 1. sin(2pix/a) wave functions
[1] Determine all potentials V(r0,) for which it is possible to find solutions of the time-independent Schroedinger equation which are also eigenfunctions of the operator L. (Help: The operator expression of the Hamiltonian for a particle of mass m in threedimensions is given (r))- 2m r ar2 1,2 2mr2 [1] Determine all potentials V(r0,) for which it is possible to find solutions of the time-independent Schroedinger equation which are also eigenfunctions of the operator L. (Help: The operator expression of...
Consider the following second order linear operator: 82 with Notice, that if instead of 3 we had 2 there, we would get a Legendre operator (whose eigenfunctions are Legendre polynomials). But nothing can be further from it than the operator above. The eigenvalue/eigenfunction problem, emerged in the analysis of vibrations of a particular quant urn liquid. An eigenvalue λ corresponds to an excitation mode of frequency Ω = V The eigenfunction ψ(r) would give a spatial profile of the deviation...
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)
Find the eigenvalues and eigenfunctions for the differential operator L(y)=−y″L(y)=−y″ with boundary conditions y′(0)=0y′(0)=0 and y′(3)=0y′(3)=0, which is equivalent to the following BVP y″+λy=0,y′(0)=0,y′(3)=0.y″+λy=0,y′(0)=0,y′(3)=0. Find the eigenvalues and eigenfunctions for the differential operator L(y)--y" with boundary conditions y (0)0 and y' (3)-0, which is equivalent to the following BVP (a) Find all eigenvalues 2n as function of a positive integer n > 1. (b) Find the eigenfunctions yn corresponding to the eigenvaluesn found in part (a). Help Entering Answers ew...
Quadrant(s) in which y = sin x decreases and y = cos x increases. Check all 1 point that apply. * OQI Q11 000 1 point Quadrant(s) in which y = cos x is BOTH increasing and negative. Check all that apply. * OQI O QUI O QIII O QIV Quadrant(s) in which y = tan x is BOTH increasing and negative. Check all that apply. * 1 point OQI O QUI O O O QIII QIV O 1 point...
Which of the following statements are true? Select all that apply. 1.) For any quantum mechanical problem, the set of eigenfunctions is larger than the set of wave functions. 2.) The set of all wave functions must satisfy the boundary conditions as well as satisfy the conditions that allow us to interpret the square of the magnitude of the wave function in terms of probability. 3.) For any quantum mechanical problem, the set of wave functions is larger than the...
Which of the following are functions of magnesium in the human body? Check all that apply. Check All That Apply A.Helps regulate heart and nerve functioning B.Cofactor for certain enzymes C. Acts as an antioxidant D.Helps regulate blood pressure and blood glucose levels E.Maintenance of fat tissue