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(2.1) (20 points) A spin 1/2 particle is in an eigenstate of Sy with eigenvalue h/2...
(7) Consider a spin-1/2 particle that is in the eigenstate of S,. The sys- tem is...
(7) Consider a spin-1/2 particle that is in the eigenstate of S,. The sys- tem is rotated by an angle 0 = T/4 about z axis. What is. (a) State of the system after rotation?? (b) What are the expectation values of S2, S, and S̟ after rotation ??
1 2. Consider the normalized spin state To (31t) +i\L)) (2) 10 (a) Is this state...
1 2. Consider the normalized spin state To (31t) +i\L)) (2) 10 (a) Is this state lx) an eigenstate of $2 ? Is it an eigenstate of Ŝe ? (Justify your answers.) In each case, if it is an eigenstate, give the eigenvalue. (b) If the spin state is as given above, and a measurement is made of the 2-component of the angular momentum, what are the possible results of that measurement and what are probabilities of each possible result?...
Problem 111.3. A spin 1/2 particle interacts with a nnagnetic field B = Boe through the...
Problem 111.3. A spin 1/2 particle interacts with a nnagnetic field B = Boe through the Pauli interaction H-μσ. B where μ is the magnetic moment. The Pauli spin matrices are İ-(Oz,@yMwwhere the σί are T0 1 0-il The eigenstates for d, are the spinors 0 (a) (3 pts.) Suppose that at time t-0 the particle is in an eigenstate Xx corresponding to spin pointing along the positive z-axis. Find the eigenstatexz in terms of α and β. (b) (7...
Problem 2. (20 points) Consider a spin-1/2 particle with gyromagnetic ratio γ in a magnetic field B- Bi+B,k . (a) Treat...
Problem 2. (20 points) Consider a spin-1/2 particle with gyromagnetic ratio γ in a magnetic field B- Bi+B,k . (a) Treating Bi as a perturbation, (i) (6 points) calculate the first-order and second-order shift in energy and (ii) (4 points) calculate the first-order energy shift in wave function for the ground state. (b) (10 points) Solve the energy eigenvalue problem exactly, and compare the exact answers expended to the corresponding orders.
Problem 2. (20 points) Consider a spin-1/2 particle with...
1. (20 points) Using the eigenstates of S, as the basis, (a) determine the eigenvalues and...
1. (20 points) Using the eigenstates of S, as the basis, (a) determine the eigenvalues and eigenstates of Sy; (b) determine the eigenvalues and eigenstates of S.ñ, where S is the spin-1/2 angular momentum, ñ is an unit vector. 2.(30 points) Consider a system with j = 1. (a) Explicitly write down <j = 1, m'J j = 1, m > in 3 x 3 matrix form. (b) Determine the eigenstate and eigenvectors of Jr. (c) Consider the eigenstate of...
1. In this problem, we are going to look at a three-level system. A spin-1 particld is placed in ...
1. In this problem, we are going to look at a three-level system. A spin-1 particld is placed in a constant magnetic field along the a-direction with strength B,. The spin-1 particle İs initialized in a z-eigenstate with positive eigenvalue h, ie, the i 1,m 1) state. What is the probability to find the negative eigenvalue the spin along the z axis as a function of time? Assume that the spin-1 particle has inagnetic moment 2 × μιι, i.e. that...
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...
The behavior of a spin- particle in a uniform magnetic field in the z-direction, , with...
The behavior of a spin-
particle in a uniform magnetic field in the z-direction,
, with the Hamiltonian
You found that the expectation value of the spin vector
undergoes Larmor precession about the z axis. In this sense, we can
view it as an analogue to a rotating coin, choosing the
eigenstate with eigenvalue
to represent heads and the eigenstate with eigenvalue
to represent tails. Under time-evolution in the magnetic field,
these eigenstates will “rotate” between each other.
(a) Suppose...
please do questions g and h... ONLY G AND H The three spin operators for an...
please do questions g and h... ONLY G AND H
The three spin operators for an electron (which is a spin-1/2 particle) are $. - 1 (1 :). $=(: ;), $- (-). Suppose the electron is pinned in space but is subject to a magnetic field B = (0,0,B), so that its Hamiltonian H = -1B-S = - BS. Suppose an initial state of the electron is prepared so that (0)) = (?) a. Show that (0)) is a unit...
pls solve asap .. thanks A spin-particle is fixed in space with the Hamiltonian H =...
pls solve asap .. thanks
A spin-particle is fixed in space with the Hamiltonian H = as, + b($+$3), where a and b are constants and as usual, Sx, Sy, S, are the operators which gives the x-, y-, z-components of the total spin. a) Write the matrix representation of Hamiltonian, H. [6 marks] b) Determine the energy levels of this system. [2 marks] c) List all possible energy levels of this system [2 marks] (Show proper construction of the...
(7) Consider a spin-1/2 particle that is in the eigenstate of S,. The sys- tem is rotated by an angle 0 = T/4 about z axis. What is. (a) State of the system after rotation?? (b) What are the expectation values of S2, S, and S̟ after rotation ??
1 2. Consider the normalized spin state To (31t) +i\L)) (2) 10 (a) Is this state lx) an eigenstate of $2 ? Is it an eigenstate of Ŝe ? (Justify your answers.) In each case, if it is an eigenstate, give the eigenvalue. (b) If the spin state is as given above, and a measurement is made of the 2-component of the angular momentum, what are the possible results of that measurement and what are probabilities of each possible result?...
Problem 111.3. A spin 1/2 particle interacts with a nnagnetic field B = Boe through the Pauli interaction H-μσ. B where μ is the magnetic moment. The Pauli spin matrices are İ-(Oz,@yMwwhere the σί are T0 1 0-il The eigenstates for d, are the spinors 0 (a) (3 pts.) Suppose that at time t-0 the particle is in an eigenstate Xx corresponding to spin pointing along the positive z-axis. Find the eigenstatexz in terms of α and β. (b) (7...
Problem 2. (20 points) Consider a spin-1/2 particle with gyromagnetic ratio γ in a magnetic field B- Bi+B,k . (a) Treating Bi as a perturbation, (i) (6 points) calculate the first-order and second-order shift in energy and (ii) (4 points) calculate the first-order energy shift in wave function for the ground state. (b) (10 points) Solve the energy eigenvalue problem exactly, and compare the exact answers expended to the corresponding orders.
Problem 2. (20 points) Consider a spin-1/2 particle with...
1. (20 points) Using the eigenstates of S, as the basis, (a) determine the eigenvalues and eigenstates of Sy; (b) determine the eigenvalues and eigenstates of S.ñ, where S is the spin-1/2 angular momentum, ñ is an unit vector. 2.(30 points) Consider a system with j = 1. (a) Explicitly write down <j = 1, m'J j = 1, m > in 3 x 3 matrix form. (b) Determine the eigenstate and eigenvectors of Jr. (c) Consider the eigenstate of...
1. In this problem, we are going to look at a three-level system. A spin-1 particld is placed in a constant magnetic field along the a-direction with strength B,. The spin-1 particle İs initialized in a z-eigenstate with positive eigenvalue h, ie, the i 1,m 1) state. What is the probability to find the negative eigenvalue the spin along the z axis as a function of time? Assume that the spin-1 particle has inagnetic moment 2 × μιι, i.e. that...
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...
The behavior of a spin-
particle in a uniform magnetic field in the z-direction,
, with the Hamiltonian
You found that the expectation value of the spin vector
undergoes Larmor precession about the z axis. In this sense, we can
view it as an analogue to a rotating coin, choosing the
eigenstate with eigenvalue
to represent heads and the eigenstate with eigenvalue
to represent tails. Under time-evolution in the magnetic field,
these eigenstates will “rotate” between each other.
(a) Suppose...
please do questions g and h... ONLY G AND H
The three spin operators for an electron (which is a spin-1/2 particle) are $. - 1 (1 :). $=(: ;), $- (-). Suppose the electron is pinned in space but is subject to a magnetic field B = (0,0,B), so that its Hamiltonian H = -1B-S = - BS. Suppose an initial state of the electron is prepared so that (0)) = (?) a. Show that (0)) is a unit...
pls solve asap .. thanks
A spin-particle is fixed in space with the Hamiltonian H = as, + b($+$3), where a and b are constants and as usual, Sx, Sy, S, are the operators which gives the x-, y-, z-components of the total spin. a) Write the matrix representation of Hamiltonian, H. [6 marks] b) Determine the energy levels of this system. [2 marks] c) List all possible energy levels of this system [2 marks] (Show proper construction of the...
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