![3) An electron whose spin is quatized in n = (sin (1) cos (0), sin (1) sin (0), cos (7)] is in a magnetic field B = (0,0, Bo)](http://img.homeworklib.com/questions/ffee0800-ad53-11eb-8b08-87cdbe50c521.png?x-oss-process=image/resize,w_560)
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3) An electron whose spin is quatized in n = (sin (1) cos (0), sin (1)...
4.8. A spin- particle, initially in a state with S h/2 with n sin i+ cos...
4.8. A spin- particle, initially in a state with S h/2 with n sin i+ cos k, is in a constant magnetic field Bo in the z direction. Determine the state of the particle at time and determine how (S,), (S), and (S.) vary with time.
) cos(0/2) + -2) state is placed in a magnetic field with strength B pointing 4....
) cos(0/2) + -2) state is placed in a magnetic field with strength B pointing 4. Larmor precession: an electron prepared in the V(t 0 sin(0/2)e in the a-direction. Calculate the time evolution of the electron's spin state. In addition calculate the time evolution of (S), S and (S ). (2 points)
1. The aim of this problem set is to understand the dynamics of a spin-1/2 system...
1. The aim of this problem set is to understand the dynamics of a spin-1/2 system in its full glory. Note that formally a spin-1/2 system and a qubit are equivalent hence, all what you will discover in this problem set will carry over to single qubits. Consider an electron spin (spin 1/2, magnetic moment gHB) interacting with a strong magnetic field Bo (0,0, B) in the z direction as well as with a much weaker magnetic field Brf =...
Consider an electron whose wave function is ?(r,0,?)-- e* sin ? + cos ?)f(r). 47t where...
Consider an electron whose wave function is ?(r,0,?)-- e* sin ? + cos ?)f(r). 47t where I (rrr2dr-| , and ?, ? are the azimuth and polar angles, respectively. (i) Rewrite the wave function in terms of the appropriate spherical harmonics. (4 marks) (ii) What are the possible measurement results of the z-component L, of the angular momentum of the electron in this state? (6 marks) (iii) Calculate the probability of obtaining each of the possible results in part (i)....
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...
1. Consider a spin-0 particle of mass m and charge q moving in a symmetric three-dimensional harm...
1. Consider a spin-0 particle of mass m and charge q moving in a symmetric three-dimensional harmonic oscillator potential with natural frequency W.Att-0 an external magnetic field is turned on which is uniform in space but oscillates with temporal frequency W as follows. E(t)-Bo sin(at) At time t>0, the perturbation is turned off. Assuming that the system starts off at t-0 in the ground state, apply time-dependent perturbation theory to estimate the probability that the system ends up in an...
5. Let's familiarize ourselves with the rotational Hamiltonian a bit more: 1 024(0) sin(0) O.. 24(0)...
5. Let's familiarize ourselves with the rotational Hamiltonian a bit more: 1 024(0) sin(0) O.. 24(0) 21E 250 4(0) 202 + yo) sin(0) 20 = 72 sin?(O) In the last problem set you analyzed the l = 1, m = 1 wavefunction. Let's do a harder one this time. a. If YO.4(0) = sin_(O) .ezid, what is m? Can you guess what l is equal to? Hint, the (2 pts) energy is E = 3 b. Now can you show...
1) (35 points) The wave function for a particle moving along x axis between the limits 0 and L is: (x)-C sin (nx xL) where n are 1, 2, 3, A) Determine the normalization constant C B) Why can'...
1) (35 points) The wave function for a particle moving along x axis between the limits 0 and L is: (x)-C sin (nx xL) where n are 1, 2, 3, A) Determine the normalization constant C B) Why can't n take the value of 0, briefly explain C) For n-3 determine the values of x (in terms of L) that correspond to a maximum or a minimum in the wave function D) For n-3 determine the values of x (in...
"A Watch t use 0.62/1.25 points 1 Prefous Anewe LaPCalc 10 B.018 Consider the follewing. x-3 cos 0 y5 sin...
"A Watch t use 0.62/1.25 points 1 Prefous Anewe LaPCalc 10 B.018 Consider the follewing. x-3 cos 0 y5 sin 8 (a) Sketch the curve represented by the parametric equations (indicate the orlentation of the curve) y 10 -2 21 2 -10 21 -10 (b) Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve Adjust the domain of the resuting rectangular eqvation if necessary oed Heln? 0/1.25 points | Previous Answers LarPCalc8 10.6.042 6. Find...
4.8. A spin- particle, initially in a state with S h/2 with n sin i+ cos k, is in a constant magnetic field Bo in the z direction. Determine the state of the particle at time and determine how (S,), (S), and (S.) vary with time.
) cos(0/2) + -2) state is placed in a magnetic field with strength B pointing 4. Larmor precession: an electron prepared in the V(t 0 sin(0/2)e in the a-direction. Calculate the time evolution of the electron's spin state. In addition calculate the time evolution of (S), S and (S ). (2 points)
1. The aim of this problem set is to understand the dynamics of a spin-1/2 system in its full glory. Note that formally a spin-1/2 system and a qubit are equivalent hence, all what you will discover in this problem set will carry over to single qubits. Consider an electron spin (spin 1/2, magnetic moment gHB) interacting with a strong magnetic field Bo (0,0, B) in the z direction as well as with a much weaker magnetic field Brf =...
Consider an electron whose wave function is ?(r,0,?)-- e* sin ? + cos ?)f(r). 47t where I (rrr2dr-| , and ?, ? are the azimuth and polar angles, respectively. (i) Rewrite the wave function in terms of the appropriate spherical harmonics. (4 marks) (ii) What are the possible measurement results of the z-component L, of the angular momentum of the electron in this state? (6 marks) (iii) Calculate the probability of obtaining each of the possible results in part (i)....
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...
1. Consider a spin-0 particle of mass m and charge q moving in a symmetric three-dimensional harmonic oscillator potential with natural frequency W.Att-0 an external magnetic field is turned on which is uniform in space but oscillates with temporal frequency W as follows. E(t)-Bo sin(at) At time t>0, the perturbation is turned off. Assuming that the system starts off at t-0 in the ground state, apply time-dependent perturbation theory to estimate the probability that the system ends up in an...
5. Let's familiarize ourselves with the rotational Hamiltonian a bit more: 1 024(0) sin(0) O.. 24(0) 21E 250 4(0) 202 + yo) sin(0) 20 = 72 sin?(O) In the last problem set you analyzed the l = 1, m = 1 wavefunction. Let's do a harder one this time. a. If YO.4(0) = sin_(O) .ezid, what is m? Can you guess what l is equal to? Hint, the (2 pts) energy is E = 3 b. Now can you show...
1) (35 points) The wave function for a particle moving along x axis between the limits 0 and L is: (x)-C sin (nx xL) where n are 1, 2, 3, A) Determine the normalization constant C B) Why can't n take the value of 0, briefly explain C) For n-3 determine the values of x (in terms of L) that correspond to a maximum or a minimum in the wave function D) For n-3 determine the values of x (in...
"A Watch t use 0.62/1.25 points 1 Prefous Anewe LaPCalc 10 B.018 Consider the follewing. x-3 cos 0 y5 sin 8 (a) Sketch the curve represented by the parametric equations (indicate the orlentation of the curve) y 10 -2 21 2 -10 21 -10 (b) Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve Adjust the domain of the resuting rectangular eqvation if necessary oed Heln? 0/1.25 points | Previous Answers LarPCalc8 10.6.042 6. Find...
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