
QUESTION 14 The wavefunction of f(x) - 2cos(x) is an eigenfunction of the Hamiltonian a true...
For each pair, determine if the wavefunction is an eigenfunction of the operator listed. If the wavefunction is an eigenfunction of the operator, clearly identify the corresponding eigenvalue. (a) = + + = Aerky a pika w piks z (b) 3 = tan(ka) 4 = sin(km) Note: tan(x) = 3
8. Consider one electron in a 1D box of side L. Its wavefunction is given by V3 V3 2V3i where ф1(x), фг(x), and фз(x) are the first 3 eigenfunctions of the Hamiltonian, A, of a particle in a 1D box, h2 d2 a) Is Ψ(x) normalized? If it is not normalized it, normalize it! b) Is ų (x) an eigenfunction of A? If it is an eigenfunction, what is the eigenvalue?
11. Circle true or false. No justification is needed. (14 points) (a) If f(x) - o(g(x), and both functions are continuous and positive, then fix dz converges. TRUE FALSE (b) If f(x)- o(g(x)), then f(x)gx)~g(x). TRUE FALSE (c) If the power series Σ an(x + 2)" converges atェ= 5, then it must km0 converge at =-6. TRUE FALSE (d) There exists a power series Σ akz" which converges to f(z)-I on some interval of positive length around FALSE TRUE (e)...
Question 5 12 pts Claim: The graph pictured below has an Hamiltonian circuit. O True O False Question 6 12 pts Claim: There exists a graph with 4 vertices with degrees 1, 1, 3, 3. O True O False Question 7 12 pts Claim: The graph pictured below has an Euler circuit. O True O False Question 8 12 pts Claim: The graph pictured below has an Euler circuit. O True O False
8. Consider one electron in a 1D box of side L. Its wavefunction is given by из where ф1(x), фг(x), and фз(x) are the first 3 eigenfunctions of the Hamiltonian, H, of a particle in a 1D box, 2m dx2 a) Is Ψ(x) normalized? If it is not normalized it, normalize it! b) Is Ψ(x) an eigenfunction of A? If it is an eigenfunction, what is the 9. A linear polyene contains 8 -electrons, and absorbs light with412 nm. b)...
A Hamiltonian Cycle is any loop within a graph. A True False Question 25 2.38 Points A loop is a graph with n vertices connected with n-1 edges. True B False 2.38 Points Question 26 A minimum spanning tree is a loop. I E True B False
Please finish this question with step-by-step details, thx!
Consider one electron in a 1D box of side L. Its wavefunction is given by V3 /3 A. where φ1(x),P2(x), and φ3(x) are the first 3 eigenfunctions of the Hamiltonian, H, of a particle in a 1D box, h2 d2 2mdx2 Az- a) ls (x) normalized? If it is not normalized it, normalize it! b) is Ψ(x) an eigenfunction of H? If it is an eigenfunction, what is the eigenvalue?
QUESTION 9 log8 (16)-1098 (2) = O 14 QUESTION 10 True or False: The domain of the log function is all real numbers. O True ︶ False QUESTION 11 What is the domain of the function f(x) -In (x-3) all real numbers
Question 8 (Chapters 1-8) [1 x 14 14 marks For the statements bellow, say if they are true or false. If true, give a short mathematical proof, if false, give a counterexample. (h) If f : Rn → R is convex and h : R → Rnxn s strictly convex and nondecreasing, then ho f is strictly convex (i) If f is strictly convex, then it is coercive. ) If f : Rn → R is such that the level...
Question 14 1 pts TRUE/FALSE: In order to optimize a differentiable function f(x, y)over the disk (filled in circle) x2 + y2 < 4, you first find all critical points in that disk, and then sort them by output. Then, you use the method of Lagrange Multipliers (perhaps) to optimize the function on the boundary circle. Finally, you compare all special points and circle the biggest/smallest outputs and type them into webassign. True O False