3 of 5 Problem #2 (show all your work!) spin For the state +), calculate the...
An electron is in the spin state x= A () (a) Determine the normalization constant A. (b) Find the expectation values of Sx , Ŝ, and Ŝ. (c) Find the “uncertainties” Ost, Os, and os, (d) Confirm that your results are consistent with all three uncertainty principles.
b 2. Suppose a spin-2 particle is in the state that particle. 2,0) + 2,1) Find the expectation value of S, for D 3. In the t spin-1/2 basis, consider the two operators 2 1 12d B- (2 i A= ni 2 (a) Find the commutator [A, B (b) Suppose we measure a number of particles in state |t), using A and B. Find the average values (A) and (B) from these measurements. (c) Use the uncertainty principle to find...
1 2. Consider the normalized spin state To (31t) +i\L)) (2) 10 (a) Is this state lx) an eigenstate of $2 ? Is it an eigenstate of Ŝe ? (Justify your answers.) In each case, if it is an eigenstate, give the eigenvalue. (b) If the spin state is as given above, and a measurement is made of the 2-component of the angular momentum, what are the possible results of that measurement and what are probabilities of each possible result?...
1-3i An electron is in the spin state x A a. Determine the normalization constant A b. Find the expectation value for S c. Find the expectation values for Sx d. Find the expectation values for Sz e. If you measure S on this electron, what values you get, and what is the probability of cachn? f. If you measure on this electron, what values you get, and what is the probability of cachn? g. If you measure Sy on...
Calculate the spin-only and spin-orbit magnetic moment for Cu2+ (show all work)
Calculate the spin quantum number (S), which is the sum of all the single electron spins for each spin state in the problem above. For the high spin case given above S=5/2 and for the low spin case S=1/2. Give an example of a metal and its oxidation state for each splitting diagram
Please solve question 3 ,4,5,6 the state IL,tni is an eigenvestor of i and izg with eigeanvalues of +1) and mzh, respectively. Find L>and<I2> n electron is placed in a uniform magnetic field B Bok. At time t O S, was measured and was found to be h/2. (a) (5 points) Write its spin wavefunction at any later time t. (b) (5 points) Calculate < S () (5 pointa) At what time t if you mensure the y component of...
suppose a quanton has a spin state [4/5 -3/5] what is the probability we will determine a quanton in such a state to have sy = -1/2h?
Problem 3: A free particle of mass m in one dimension is in the state Hbr Ψ(z, t = 0) = Ae-ar with A, a and b real positive constants. a) Calculate A by normalizing v. b) Calculate the expectation values of position and momentum of the particle at t 0 c) Calculate the uncertainties ΔΧ and Δ1) for the position and momentum at t 0, Do they satisfy the Heisenberg relation? d) Find the wavefunction Ψ(x, t) at a...
[ 2 + 3 + 3 + 5 = 13 marks ] Question 4 (a) For the case of two qubits, briefly explain the main difference between product states and entangled states. Provide one example of each. (b) Show that the identity between spin angular momentum operators S+S- = S2- S2 ± hS, holds. Data: S S tiSy, [Se, Sy] = ihS2, [Sy, S2] = ihS, [S2, S = ihSy. (c) An s = 1/2 particle at t =0 is...