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2. Interacting Spins (5 points each part, 30 points total). Two spins, each of which can...
The system, which consists of N spins, each of which has a magnetic moment of μo...
The system, which consists of N spins, each of which has a magnetic moment of μo and a spin quantum number of 1/2, is placed within the B magnetic field. Find the expression that gives the chemical potential (μ (T)) by using the expression that gives the state of the system's input (hint: use Ω(N,n)=Ω(N,0)*e^(-2n^2/N) to find the states of the system.)
The energy of a magnetic moment in a magnetic field is . A certain paramagnetic salt contai...
The energy of a magnetic moment in a magnetic field is . A certain paramagnetic salt contains 1025 magnetic moments per m3. Each one has a value , due to the atom's spin. As the spin is 1/2, there only are two possible states and the magnetic moments can be parallel or antiparallel to the field. Each magnetic moment belongs to one distinguishable atom. A 1 cm3 sample of this salt is placed in a electromagnet producing a uniform magnetic...
3.3 One spin in thermal contact with a large spin system Generalize the preceding problem by...
3.3 One spin in thermal contact with a large spin system Generalize the preceding problem by considering the case where the system A' consists of some arbitrarily large number N of spins J, each having magnetic moment plo. The system A consists again of a single spin { with mag- netic moment Mo. Both A and A' are located in the same magnetic field B and are placed in contact with each other so that they are free to exchange...
Consider one dimensional lattice of N particles having a spin of 1 /2 with an associated magnetic...
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...
1. (30 points). Coupled spins. Spin-1/2 particles A and B evolve under the influence of the follo...
1. (30 points). Coupled spins. Spin-1/2 particles A and B evolve under the influence of the following Hamiltonian (for simplicity takeh-1 so that energies are expressed in frequency units): We work in the uncoupled basis aba) Ib), where a,b E 0,1 and where states 0) (1)) correspond to single spins aligned (antialigned) with the z-direction. As we discussed in lecture, the eigenstates of the Hamiltonian are 100), 111), and 2-1/2 (101) 110)). a. We prepare the initial state t01). Since...
3. In one experiment, the maximum magnetic field is 2 Tesla and the initial temperature is 300 K....
3. In one experiment, the maximum magnetic field is 2 Tesla and the initial temperature is 300 K. Pretending that a nucleus has only two possible spin states, calculate the magnetization per particle, M/N, for this system. Take nuclear magnetic moment μ to be 5 x 108 ev/T. One can use resonant radio waves to detect such magnetizations. Calculate the energy that a radio wave photon should have to flip a single nucleus from one magnetic state to the other....
why total orbitals are 6 ?? and please answer the number of orbitals of self test...
why total orbitals are 6 ?? and please answer the number of
orbitals of self test 9c.3
No Brief illustration 90.3 Spin-orbit coupiny The unpaired electron in the ground state of an alkali metal atom has l=0, so j=1. Because the orbital angular momen- tum is zero in this state, the spin-orbit coupling energy is zero (as is confirmed by settingj=s and 1=0 in eqn 9C.4). When the electron is excited to an orbital with I=1, it has orbital angular...
qm 2019.3 3. The Hamiltonian corresponding to the magnetic interaction of a spin 1/2 particle with...
qm 2019.3
3. The Hamiltonian corresponding to the magnetic interaction of a spin 1/2 particle with charge e and mass m in a magnetic field B is À eB B. Ŝ, m where Ŝ are the spin angular momentum operators. You should make use of expres- sions for the spin operators that are given at the end of the question. (i) Write down the energy eigenvalue equation for this particle in a field directed along the y axis, i.e. B...
2. Consider an isolated system consisting of a large number N of very weakly interacting localized...
2. Consider an isolated system consisting of a large number N of very weakly interacting localized particles of spin 1 2. Each particle has a rnagnetic mioment μ which can point parallel or anti-parallel to an applied field H. The energy E of the systern is then E =-(ni-n2):1H, antiparallel to H. (a) Consider the energy range between E and E+δΕ where δΕ < E but is microscopically large so that δΕ μΗ. What is the total number of states...
Question 9 Consider a quantum system comprising two indistinguishable particles which can occupy only three individual-particle...
Question 9 Consider a quantum system comprising two indistinguishable particles which can occupy only three individual-particle energy levels, with energies 81 0, 82 2 and E3 38.The system is in thermal equilibrium at temperature T. (a) Suppose the particles which can occupy an energy level. are spinless, and there is no limit to the number of particles (i) How many states do you expect this system to have? Justify your answer (ii) Make a table showing, for each state of...
3.3 One spin in thermal contact with a large spin system Generalize the preceding problem by considering the case where the system A' consists of some arbitrarily large number N of spins J, each having magnetic moment plo. The system A consists again of a single spin { with mag- netic moment Mo. Both A and A' are located in the same magnetic field B and are placed in contact with each other so that they are free to exchange...
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...
1. (30 points). Coupled spins. Spin-1/2 particles A and B evolve under the influence of the following Hamiltonian (for simplicity takeh-1 so that energies are expressed in frequency units): We work in the uncoupled basis aba) Ib), where a,b E 0,1 and where states 0) (1)) correspond to single spins aligned (antialigned) with the z-direction. As we discussed in lecture, the eigenstates of the Hamiltonian are 100), 111), and 2-1/2 (101) 110)). a. We prepare the initial state t01). Since...
3. In one experiment, the maximum magnetic field is 2 Tesla and the initial temperature is 300 K. Pretending that a nucleus has only two possible spin states, calculate the magnetization per particle, M/N, for this system. Take nuclear magnetic moment μ to be 5 x 108 ev/T. One can use resonant radio waves to detect such magnetizations. Calculate the energy that a radio wave photon should have to flip a single nucleus from one magnetic state to the other....
why total orbitals are 6 ?? and please answer the number of
orbitals of self test 9c.3
No Brief illustration 90.3 Spin-orbit coupiny The unpaired electron in the ground state of an alkali metal atom has l=0, so j=1. Because the orbital angular momen- tum is zero in this state, the spin-orbit coupling energy is zero (as is confirmed by settingj=s and 1=0 in eqn 9C.4). When the electron is excited to an orbital with I=1, it has orbital angular...
qm 2019.3
3. The Hamiltonian corresponding to the magnetic interaction of a spin 1/2 particle with charge e and mass m in a magnetic field B is À eB B. Ŝ, m where Ŝ are the spin angular momentum operators. You should make use of expres- sions for the spin operators that are given at the end of the question. (i) Write down the energy eigenvalue equation for this particle in a field directed along the y axis, i.e. B...
2. Consider an isolated system consisting of a large number N of very weakly interacting localized particles of spin 1 2. Each particle has a rnagnetic mioment μ which can point parallel or anti-parallel to an applied field H. The energy E of the systern is then E =-(ni-n2):1H, antiparallel to H. (a) Consider the energy range between E and E+δΕ where δΕ < E but is microscopically large so that δΕ μΗ. What is the total number of states...
Question 9 Consider a quantum system comprising two indistinguishable particles which can occupy only three individual-particle energy levels, with energies 81 0, 82 2 and E3 38.The system is in thermal equilibrium at temperature T. (a) Suppose the particles which can occupy an energy level. are spinless, and there is no limit to the number of particles (i) How many states do you expect this system to have? Justify your answer (ii) Make a table showing, for each state of...
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