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[ 2 + 2 + 2 + 3 + 3 = 12 marks ] Question 5 (a) Briefly explain why we cannot find simultaneous eigenfunctions of Lt, L...
Question 5 [2 + 2 + 2 + 3 + 3 = 12 marks ] (a) Briefly explain why we cannot find simultaneous eigenfunctions of Lg, Ly and Lz. An electron in a hydrogen atom is in the n = 2 state. Ignoring spin, write down the list of possible quantum numbers {n, l, m}. (b) For two qubits briefly explain, giving examples, the difference between a product state and an entangled state (c) Consider a system of identical bosons...
[1 44= 9 marks ] Question 5 Consider two identical particles in 1D which exist in single-particle (normalised) (x), and are in such close proximity they can be considered as indistinguishable. wave functions /a(x) and (a) Write down the symmetrised two-particle wave function for the case where the particles are bosons (VB) and the case where the particles are fermions (Vp). (b) Show that the expectation value (xjr2)B,F is given by: (T122) в,F — (а:)a (х)ь + dx x y:(")...
[ 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...
1) (35 points) The wave function for a particle moving along x axis between the limits 0 and L is: (x)-C sin (nx xL) where n are 1, 2, 3, A) Determine the normalization constant C B) Why can't n take the value of 0, briefly explain C) For n-3 determine the values of x (in terms of L) that correspond to a maximum or a minimum in the wave function D) For n-3 determine the values of x (in...
2.(a). By considering a circuit containing a capacitor shown below, explain briefly why Ampere's law B.dr Ho,1(S,) needs to be modified to allow for time-varying fields. What modification is needed to correct the equation? [3] -Q I s, is a surface bounded by the curve C and cutting the wire. (b). The magnetic field in free space due to a monochromatic plane wave is of the form: B(x, y,z,t) B, cos(kz-ax) where Bo, k and ware constants. Write down the...
Question 1 (8 marks in total) The deuteron is a bound state of a proton and a neutron. Treating nucleons as identical particles with spin and isospin degrees of freedom, the total state of the deuteron can be writ- ten space Ψ spin Ψ isospin. The deuteron has a total angular momentum quantum number J - 1 and a total spin S -1. Our goal is to determine the parity of the deuteron Q1-1 (1 mark) Show that the possible...
Question 8 please 5. We start with Schrodinger's Equation in 2(x,t) = H¥(x,t). We can write the time derivative as 2.4(x, t) = V(x,+) - (xt), where At is a sufficiently small increment of time. Plug the algebraic form of the derivative into Schrodinger's Eq. and solve for '(x,t+At). b. Put your answer in the form (x,t+At) = T '(x,t). c. What physically does the operator T do to the function '(x,t)? d. Deduce an expression for '(x,t+24t), in terms...
question number 5 6. Suppose that the electron in a hydrogen atom is perturbed by a repulsive potential concentrated at the origin. Assume the potential has the form of a 3-dimensional delta function, so the perturbed Hamiltonian is pe? H +.48°(r). 2m T where A is a constant. To first order in A, find: (a) the change in the energy of the state with quantum numbers n = 1,1 = 0. Hint: 1100(r) = 2 exp(-r/ao) 3/2 V4π αο (b)...
(15 points) Encounter with a semi-infinite potential "well" In this problem we will investigate one situation involving a a semi-infinite one-dimensional po- tential well (Figure 1) U=0 region 1 region 2 region 3 Figure 1: Semi-infinite potential for Problem 3 This potential is piecewise defined as follows where Uo is some positive value of energy. The three intervals in x have been labeled region 1,2 and 3 in Figure 1 Consider a particle of mass m f 0 moving in...
Part B All this are multiple questions Part C Part D Part E Question 3 (MCQ QUESTION) [8 Marks) A hypothetical quantum particle in 10 has a normalised wave function given by y(x) = a.x-1.b, where o and bare real constants and i = V-1. Answer the following: a) What is the most likely x-position for the particle to be found at? Possible answers forder may change in SAKAI 14] a - b + ib a 0 Question 3 (MCQ...