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For a system of two particles with spin 3/2 and 1/2 write out all the possible...
Exercise 8.3 (a) Write down all possible states of two nonidentical particles of spin 1 (i.e., both particles are in s states). (b) What restrictions do we get if the two particles are identical. Write down all possible states for this system of two spin 1 identical particles.
System A consists of two spin-1/2 particles, and has a four-dimensional Hilbert space. 1. Write down a basis for the Hilbert space of two spin-1/2 particles. 2. Calculate the matrix of the angular momentum operator, Sfot = (ŜA, ŠA, ŜA) for system A, in the basis of question 4A.1, and express them in this basis. 3. Calculate the square of the total angular momentum of system A , Spotl?, and express this operator in the basis of question 4A.1. 4....
Problem2 Two possible wave functions for two spin 1 /2 particles with Sz = 0 are Apply the operator S+ to both states as many times as needed to find the largest possible value for m and hence determine the value of S2 for each state Problem2 Two possible wave functions for two spin 1 /2 particles with Sz = 0 are Apply the operator S+ to both states as many times as needed to find the largest possible value...
If the spin angular momenta of two spin-1 particles are added, the possible m valnes for the z-component of the total spin angular momentum (such that Š ) m)are a) m=-1,0, or 1 b) m= c) m=2.0, or-2 d) m--2-3/2,-1,-1/2, 0, 1/2, 1, 3/2, or2 e) m 2, 1, or f) none of the above 2,1, 0,1, or 2
Consider one dimensional lattice of N particles having a spin of 1 /2 with an associated magnetic moment μ The spins are kept in a magnetic field with magnetic induction B along the z direction. The spin can point either up, t, or down, , relative to the z axis. The energy of particle with spin down is e B and that of particle with spin up is ε--B. We assume that the system is isolated from. its environment so...
Starting with the following eigenket for a system of two spin-1/2 particles, obtain the other three eigenkets in the (s,m) representation. 3.
11 Consider an assembly of N-4 particles in a system which has equally spaced non degenerate energy levels, U-0.e,2e,3e, The total energy of the system is U 6. a) Assuming the particles are distinguishable, how many distributions of the particles over the energy levels are possible? List all of them in a table showing the number [7] of particles, n, in each energy level U b) To which particle statistics does this scenario correspond? c) How many microstates contribute to...
[5] A large number of spin-1/2 particles are run through a Stern-Gerlach machine. When they emerge. all particles have the same spin wave function s)- (where the vector representation is in the basis set of eigenvectors of Sz. The spin of the particles is measured in the z-direction. On average, 2/3 of the particles have spin in the +z direction and 1/3 in the z direction. (a) Determine one possible normalized spin wave functio tere a single unique solution to...
2. Addition of Angular Momentum a) (8pts) Given two spin 1/2 particles, what are the four possibilities for their spin configuration? Put your answer in terms of states such as | 11). where the first arrow denotes the z-component of the particle's spin. Identify the m values for each state. b)(7pts) If you apply the lowering operator to a state you get Apply the two-state lowering operator S--S(,) +S(), where sti) acts on the first state and S acts on...
Consider a system with 2 spin 1/2 particles. The Hamiltonian is given by: