A particle is in the eigen state of L?, L, with eigen values ħ21(1 + 1)...
3. (6 points) Measurements on a two-particle state Consider the state for a system of two spin-1/2 particles, (2]+).I+)2 +1-)[+)2-1-)1-)2). (a) Show that this state is normalized. (b) What is the probability of measuring S: (the z-component of spin for particle 1) to be +h/2? After this measurement is made with this result, what is the state of the system? If we make a measurement in this new state, what is now the probability of measuring S3 = +h/2? (e)...
Q1. Consider A = | 2 1 0 | . The eigen values of A are λ1 =-3, λ2 =-1, and λ3 = 3 and the 0 0 -3 corresponding eigen vectors are Let T- vi | v2 l v31. From linear algebra, we know that 0 0 A3 Using this relationship, compute eAt.
orbital angular momentum For an orbital angular momentum, measurement of L and Lz produces ħ²1 (1+ 1) and mħ respectively. What are the values of < Lx > and AL,? Assume 1 = 1, m probability for Lx = -ħ? 1, what is the
A particle is in the ground state of a box of length L (from -L/2 to L/2). Suddenly the box expands symmetrically to twice its size (from -L to L), leaving the wave function undisturbed. Show that the probability of finding the particle in the ground state of the new box is (8/3pi)^2.
a-obtain state space representation b-obtain system eigen values c-diagnolize the system Question (3: (10 Marks) For the following system, U(s) s + 5 (s +2) (s +3) s + 1 Obtain a state space representation in the controllable canonical form. (4 marks) b) Obtain the system eigen values, (3 marks) c) Diagonalize the system. (3 marks) a) Page 2 DQMS 2/3 Question (3: (10 Marks) For the following system, U(s) s + 5 (s +2) (s +3) s + 1...
7. The Eigen vectors and eigen values of the 2nd moment matrix in Harris detector represents, (a) The dominant edge orientation, (b) The direction where the largest changes of the pixel values will incur in the detection window, (c) The rate of change in detection window pixel average values (d) The probability of a 8. The largest Eigen Value of the 2nd moment matrix in Harris detector represents, (a) The dominant edge orientation, (b) The direction where the largest change...
3.9. A particle of mass m is confined in the potential well 0 0<x < L oo elsewhere (a) At time t 0, the wave function for the particle is the one given in Problem 3.3. Calculate the probability that a measurement of the energy yields the value En, one of the allowed energies for a particle in the box. What are the numerical values for the probabilities of obtaining the ground-state energy E1 and the first-excited-state energy E2? Note:...
(1 II. Find eigen values and eigen vectors of A=0 LO 6. 0 2 -3 01 3 2)
for a particle in a one dimensional box of length L if the particle is on the n=4 state what is the probability of finding the particle within a) 0<x<5L/6 b) L/4<x<L/2 c) 5L/6<x<L
What do you think about eigen values? What are they? When do you particularly need them? What are eigen vectors? How eigen values, unknows and eigen vectors are related ? Do you think eigen values can be complex (e.g. a+ib)? what does it mean if the eigen values are complex numbers? Please describe a problem from your daily life (you experience every day yourself) that now you have realized require eigen value analysis.