Consider a system of N spin 2 particles with allowed spin values −2,−1,0,1,2 for each particle. Compute the degeneracy factor for the case of zero total spin. Specialize to the case of N=10 for which compute the degeneracies for all possible total spin configurations. For each such configuration, draw a maximum of 10 representative examples

could you also explain to me how you come up with question A?

The essence of the statement of the uniqueness theorem is that if we know the conditions the limit that needs to be met by the potential of the system, then we find the solution of the system , then that solution is the only solution that exists and is not other solutions may be found. If we know potential solutions of a system, can we determine the type of system that generate this potential? If so, prove the statement! If no, give an example of a case that breaks the statement!

Spin/Field Hamiltonian Consider a spin-1/2 particle with a magnetic moment µ = -e/m$ placed in a uniform magnetic field aligned along the z axis. (a) Write the Hamiltonian for this system in matrix form. (b) Verify by explicit matrix calculation that the Hamiltonian does not commute with the spin operators in the r and y directions. Comment on how this affects the expectation values of these operators.

In general, a system of quantum particles can never behave even approximately like a rigid body, but non-spherical nuclei and molecules are exceptions, and have certain rotational energy levels that are well described as states of a rigid rotator whose Hamiltonian is H 21 where I is the moment of inertia, and L^ is the angular momentum operator. a, What are the eigenvalues of the angular momentum operator? b. A rigid rotator with Hamiltonian (6) is subjected to a constant perturbation V = (Ch² /21) cos² 0 ,where C is a small constant. Find the corrections to the eigenvalues and eigenfunctions to first order in perturbation theory. c. Given the perturbation condition in (b.), estimate the maximum value of C for which this is a good approximation for the level characterized by the quantum number l

A spin-2 system has 5 spin states in the Sz basis. Express the following as matrices or vectors in this basis: Ŝ2 operator, Ŝx operator, Ŝy operator, Ŝz operator, and State |2, 1⟩x (x component of spin = ħ).

Consider three noninteracting indistinguishable spin-0 particles trapped in a harmonic potential with energy states given as: [nx, Ny, nz). Consider three distinct single particle states: |0,0,0), |0,1,0), |0,2,0). Each of the particles can be in any one of the three states listed. How many different three particle states are possible?

The Hamiltonian of a spin S in a magnetic field B is given by \hspace {3cm} H = -yS · B where y is a positive constant. If a magnetic field of strength B is applied in the z– direction for a spin-half single electron system, taking @ = y B, the eigenvalues of the Hamiltonian are Select one: a. -ho, ħo O b. -hw,0, ¿ħo -ho, ho Ос. O d. -ho, ho O e. -ħw, 0, ħo

Write all the terms in the Hamiltonian operator for the Lithium atom.

A system of 9 identical non-interacting spin-3/2 particles confined to a one-dimensional harmonic oscillator potential is in its minimum energy configuration for which E 5.75 eV. What is the minimum energy of the same system with 10 such particles? Recall that the energy levels of a single particle in a one-dimensional harmonic oscillator potential are given by En = (n+1) hwo with n = 0, 1, 2, .... =