Exercise 4.7 a. Compute where the expectation value is taken for the S+)+) state, that is, Using ...
is a quantum system in the angular momentum state where is the spherical harmonics. By using generalized uncertainty principle, find value of C in where Lx and Ly are standard deviations i) what is value of C in units of ? give a comment for the ans. ii) is the state an eigenstate of (a) Lx (b) Ly (c) Lz? iii)What is the value of the standard deviation of (a) (b) (c) ? X(0,5) = 171,1(0,6) + Y1,0(0,6) + {Y1,-1(0,4),...
please show solution to 4.7 Calculate the peak value of the voltage across the inductor in figure 4.7(a), assuming Vo= 10 V, a 2t x 103 s, R= 1 2, L 25 mH, and C 1 uF. 4.6 Calculate the phase of the voltage across the inductor relative to the source in figure 4.7(a) for the values given in problem 4.6 4.7 90 Sinusoldal Circuits circuit-reducti to linear sinusoidal theorems for dc circuits can be applied cuits if the impedances...
Exercise 1: The helium atom and spin operators 26 pts (a) Show that the expectation value of the Hamiltonian in the (sa)'(2a)' excited state of helium is given by E = $42.0) (Avo ) anordes ++f63,(-) (%13-12 r) 62(e)drz + løn.(r.) per 142, (ra)]" drų dr2 - / 01.(ru) . (ra) Anemia 02.(r.)61.(r.)dr; dr2 (1) Use the approximate, antisymmetrized triplet state wave function for the (Isa)'(280)' state as discussed in class. Hint: make use of the orthonormality of the hydrogenic...
2. a) List the characteristics of turbulent flows and state why they are challenging to compute. [12 Marks b) The Navier-Stokes equations in two-dimensions for an incompressible fluid are given in part b) of Q1 above. When studying turbulent flows it is usual to time average these equations. Explain the process of time averaging and show which additional terms result from the time averaging process in two-dimensions for an incompressible fluid. 12 Marks c) When modelling turbulent flows the Navier-Stokes...
Problem 7.49 Problem 7.49 A hydrogen atom is placed in a uniform magnetic field Bo Bo (the Hamiltonian can be written as in Equation 4.230). Use the Feynman-Hellman theorem (Problem 7.38) to show that a En (7.114) where the electron's magnetic dipole moment10 (orbital plus spin) is Yo l-mechanical + γ S . μ The mechanical angular momentum is defined in Equation 4.231 a volume V and at 0 K (when they're all in the ground state) is41 Note: From...
only one problem (Exercise 1-11 only) Uncertainties in Measurement and Propagation of Errors one measurement is made and often the peecision of the instrument is used as arn mate of the uncertainty. the instrument and the situation, the uncertainty Depending upon could be less than the precision of the instrument or it could be more. For example, in measuring we may estimate the distance between the small est subdivision (mm) if we rurn the meter stick onto its side to...
for following problems please 1. compute test value and 2. find critical value (s). thanks so much! much appreciation for help with problems! Question 1 of 5 (1 point) View problem in a pop 9.2 Section Exercise 1a,b,c,d,e (critical value, up table) Is there a significant difference at a = 0.10 in the mean heights in feet of waterfalls in Europe and the ones in Asia? The data are shown. Source:World Almanac. Use the critical value method with tables. CH...
Q.3(a) Transfer function model of a plant is, G(s) The controller is Ge(s)-K, where K is a constant. Find the value of K such that steady-state error for unit ramp input is 0.1. Find the gain margin and the phase mar gin (6 marks) (b) What are the effects on gain margin, phase margin and steady-state error, if the gain K is increased? (3 marks (c) Can the closed loop be unstable if the controller of Q.3(a) is implemented digi...
Compute the following problems using Math Lab. Instructions: Answer All Questions using MATLAB commands. Question 1. Create a vector of the even whole numbers between 31 and 75. Question 2. Let x [2516] a. Add 16 to each element b. Add 3 to just the odd-index elcments c. Compute the square root of each element d. Compute the square of each element Question 3. Let x 13 268T and y [4 1 3 5] (NB. x and y should be...
A classic second order system has transfer function the undamped natural frequency to be 10 rad/s throughout this exercise. Note, for the following MATLAB simulations you need to use format long defined at the top of the program to get full precision. a) Use MATLAB to plot the step response for three damping factors of ζ =0.5,1 and 1.5 respectively. step(g,tfinal)_ where tfinal is the max time you need to make it 2 secs and g is the b) Takeζ...