From the general operator relation (given by equation 1), we can evaluate the required relation of momentum operator with the potential.
Please answer without using the graduent function (triangle). Thanks! :) Problem 1: Ehrenfest's Theorem [6 marks]...
5. A particle in the harmonic oscillator potential has the initial wave function Psi(x, 0) = A[\psi_{0}(x) + \psi_{1}(x)] for some constant A. Here to and ₁ are the normalized ground state and the first excited state wavefunctions of the harmonic oscillator, respectively. (a) Normalize (r, 0). (b) Find the wavefunction (r, t) at a later time t and hence evaluate (x, t) 2. Leave your answers involving expressions in to and ₁. c) sing the following normalized expression of...
Please answer with all steps. Thanks Given "x4 3 cos + 7 sin t 0.75_dt F(x) =let, d, G(x) =1 dt 5t0.75 0 Using the Fundamental Theorem of Calculus Part II, calculate the limit Lim Given "x4 3 cos + 7 sin t 0.75_dt F(x) =let, d, G(x) =1 dt 5t0.75 0 Using the Fundamental Theorem of Calculus Part II, calculate the limit Lim
Please answer this question Implicit Function Theorem in Two Variables: Let g: R2 - R be a smooth function. Set Suppose g(a, b)-0 so that (a, b) є S and dg(a, b) 0. Then there exists an open neighborhood of (a, b) say V such that SnV is the image of a smooth parameterized curve. (1) Verify the implicit function theorem using the two examples above (2) Since dg(a, b)メ0, argue that it suffices to assume a,b)メ0. (3) Prove the...
Can you please answer this using fundamental theorem. Thank you!! Calculus Let F(x) be the function defined on (-00,00) by the formula F(x) = L 142 – 1}dt. Find F'(x). Show your work.
problem 2 Professor A Abdurrahman's Course on Quantum Mechanics Quantum Mechanics I- Problem Set No. 3 Due to 04/30/2018. Late homework will not be accepted. Problem 1 Prove that Hint. Direct computation. Problem 2 We have been dealing with real potential V (x) so far so now suppose that V (a) is complea. Compute dt Problem 3 For the Gaussian a) 1 /4 Compute (a) (z") for all alues of n integer, and (b) Compute fors(x) given above. Hint: ?...
please answer with good handwriting Q1 (a) Given the function f(x)= x - 5x² - 2x +10. (1) Prove that there at least a root in the interval [1,3] by using Intermediate Value Theorem. (2 marks) (b) (i) Find the root of f(x) by using Bisection method. Iterate until i = 5. (8 marks) Prove the Lagrange interpolating polynomial of second degree for data of (0,1), (1,2) and (4,2) is P2(x) = -* x2 + x + 1. (5 marks)...
(Recursive Function) Display the triangle pattern without using loop. Write a recursive function named Triangle to solve the problem. void Triangle(int); Write a main function to test it. For example, a function call Triangle(6) will displays the following 6 rows of a triangle pattern. 1 1 2 1 1 2 3 2 1 1 2 3 4 3 2 1 1 2 3 4 5 4 3 2 1 1 2 3 4 5 6 5 4 3 2 1...
Answer all questions QUESTION FOUR [25 MARKS] (a) Prove that if (t, to) is the transition matrix for the systemx(t) = A(t)x(t), then the unique solution of x(t) = A(t)x(t) f(t) x(0)=xo dt with x(to)Xo some constant vector, where f(t) is a continuous function on [to, tf], is x(t) (t, to)Xo (t,)f(7) dr Jto 10 Marks (b) Hence obtain a solution to the initial value problem, given 2 1 A p2t f(t) 4 edt x(0) [15 Marks QUESTION FOUR [25...
Answer both problems please. Problem 5 Accurately sketch the following function and evaluate the integral 15 Points - (s(6-(4) W 3W x(t) A tri 3W W A tri dt Xo= Problem 6: Accurately sketch the double-sided Amplitude and Phase Spectrum of the following signal. Consider f > f 15 Points A cos(2t ft - <p)cos(2t f,t - <p,) x(t)
Mechanics. Need help with c) and d) 1. A particle of mass m moves in three dimensions, and has position r(t)-(x(t), y(t), z(t)) at time t. The particle has potential energy V(x, y, 2) so that its Lagrangian is given by where i d/dt, dy/dt, dz/dt (a) Writing q(q2.93)-(r, y, z) and denoting by p (p,P2, ps) their associated canonical momenta, show that the Hamiltonian is given by (show it from first principles rather than using the energy) H(q,p)H(g1, 92,9q3,...