a) Can a state be built from two identical particles with spin j_i = n/2 and identical spatial wavefunctions yield a J=n state?
b )The same question but with particles with j_i = n and state J = 2n
a) Can a state be built from two identical particles with spin j_i = n/2 and...
6. (Extra Credit: 6 Points) Consider two noninteracting particles of mass m in an infinite square well of width L. For the case with one particle in the single-particle state In) and the other in the state k) (nメk), calculate the expectation value of the squared inter-particle spacing (71-72) , assuming (a) the particles are distinguishable, (b) the particles are identical in a symmetrical spatial state, and (c) the particles are identical in an anti-symmetric spatial state. Use Dirac notation...
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...
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...
à 154 5. The example in question 4 was for a singlet state, which use spin 20 2px 2px 2pz wavefunctions to impart the antisymmetry property. For triplets, the This is a 1812s1 "space" wavefunctions are used to enforce the antisymmetry triplet state property. For example, the proper antisymmetric wavefunction for a 2s'1s1 spinup-spinup configuration is: (1.2) - 92s(r.)41s(2) – 42s (r2)4s(r)) 2)915}a(1)a(2) V2 2px 2py 2pz a. Let's see what happens if the two electrons are in the same...
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.
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...
Please don't just copy from somewhere. Explain clearly, even though you can skip the math part. Two identical spin-1/2 fermions of mass M are confined in a cubic box of side L. The sides of the box have infinite potential. The identical fermions interact according to the attractive potential: r1,r2 where e is small and positive, and should be treated as a perturbation. Do not neglect the effects of spin degrees of freedom in this problem. [Hint: you may or...
6. Consider two spin particles. Let nbe a unit vector joining the particles and consider the operator S12-3(?' i)(o, . n ) _ (?' ?2 ) . Show that for the singlet state its eigenvalue is 0. Show that in the triplet state its eigenvalues are -4 or 2. Choose along the z axis. (The Pauli principle is not considered.)
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...
Two non - interacting particles, with the same mass, are in a one - dimensional potential which is zero along a length 2a, and infinite elsewhere. What are the values of the four lowest energies of the system? What are the degeneracies of these energies if the two particles are: a) identical, with spin ; b) identical, with spin 1.