322 CHAPTER 5. ANGULAR MOMENTUM Problem 5.12 Consider a particle whose wave function is 1 222-x2-y2...
(V.4) A particle is observed to have orbital angular momentum quantum number 2. The z component of the angular momentum is measured to be Lz2h. A second particle is observed to have orbital angular momentum quantum number l2-2 and a z component ha = +2 V1(1 +1), what are the possible outcomes, and with what relative probabilities? What is the expectation value (L)'? h. If a measurement is made of the total angular momentum L-h
3. Consider a rigid rotor whose Hamiltonian is given by H L2(21) where L is the angular momentum operator and I is the moment of inertia of the rotator. Its rotation is described by a wave function: (0, N{Yo0(0,6)(1 3i) Y1-1(0,6) 2 Y21(0.0) Y20(0.) Find the normalization constant, N. (i) Find the probability to occupy state Yo0- (ii Find the expectation value of L2 of this state (iii Find the expectation value of L2 of this state (iv) Find (L2L2/21...
Problem N° 1 114 points] Consider two spinless particles with orbital angular momenta quantum numbers l-1 and 122. If the state of the two- particle system is described by the wave function 4 (a). Find the constant A 12 points]. (b). Find the probability that, as a result of a measurement, the system is found in a state of the form |1 1>121>112 points). Problem N° 1 114 points] Consider two spinless particles with orbital angular momenta quantum numbers l-1...
Two Particle State problem, measurement of total angular momentum, finding probabilities, action of lowering operatora) A particle of spin \(3 / 2\) and a particle of spin 1 are found in the state \(\left|\frac{3}{2}-\frac{1}{2}\right\rangle\) of total spin. Assume that the particles are in a state of zero orbital angular momentum.Find which values of the z-component of the spin of the two particles can be measured and with what probabilities.The following information applies to parts \(\mathbf{b}\) ) and \(\mathbf{c}\) ).An electron...
Consider a wave function for a hydrogen-like atom: 81 V πα3 a) Find the corresponding values of the quantum num bers n, 1, and m. (b) By measuring the angular momentum, what is the probability of finding 1-0? (c) Construct ψ(r, θ, φ) and another wave function with the same values of n and (azimuthal) quantum number, m+1 (d) Calculate the most probable value of r for an electron in the state corresponding to ψ(r, θ, φ) 1, but with...
Exercise 2:Commutators Given (AB, C) - ABC - ACB + ACB-CAB - ABC] + [A, CJB. 1- Show that the commutator[L.L]is equal to zero. 2-Computethecommutator(Ly, Lx]. 3-Compute the commutator 3.Lx]. 4-Compute the commutator[LLY.Lx]. 5- Add the results from (2)-(4) to compute [LLyLx]. Lxercise 3: Matrix elements The angular momentum operators acting on the angular momentum eigenstates. Il determined by L-11.m) = (1 + 1) - m(m + 1)2.m +1) L_11.m) = /(1+1) - mm - 1)/1.m-1) L211,m) = hm|1,m) 1-...