A measurement of a spin 1/2 observable described by the operator Sˆ = (Sˆx + Sˆy)...
A measurement of a spin 1/2 observable described by the operator Sˆ = (Sˆx + Sˆy) is made and the system is found in a state corresponding to the largest eigenvalue of Sˆ. Find the probability that at a later time, a measurement of Sˆx will yield the value +ħ/2.
Homework Answers
Add Answer to:
A measurement of a spin 1/2 observable described by the operator
Sˆ = (Sˆx + Sˆy)...
Consider a three-level system where the Hamiltonian and observable A are given by the matrix Aˆ...
Consider a three-level system where the Hamiltonian and
observable A are given by the matrix Aˆ = µ 0 1 0 1 0 1 0 1 0
Hˆ = ¯hω 1 0 0 0 1 0 0 0 1 (a) What are the possible
values obtained in a measurement of A (b) Does a state exist in
which both the results of a measurement of energy E and observable
A can be...
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...
[3] A spin-1/2 particle is in the state IW) 1/311) +i2/3|). (a) A measurement is made of the x component of the spi...
[3] A spin-1/2 particle is in the state IW) 1/311) +i2/3|). (a) A measurement is made of the x component of the spin. What is the probability that the spin will be in the +z direction? (b) Suppose a measurement is made of the spin in the z direction and it is found that the particle has m,#1/2. what is the state after the measurement? (c) Now a second measurement is made immediately after to determine the spin in the...
Consider the state of a spin-1/2 particle 14) = v1o (31+z) + i] – z)) where...
Consider the state of a spin-1/2 particle 14) = v1o (31+z) + i] – z)) where | z) are the eigenstates of the operator of the spin z-component $z. 1. Show that [V) is properly normalized, i.e. (W14) = 1. 2. Calculate the probability that a measurement of $x = 6x yields 3. Calculate the expectation value (Šx) for the state 14) and its dispersion ASx = V(@z) – ($()2. 4. Assume that the spin is placed in the magnetic...
Problem 8.3 - A New Two-State System Consider a new two-level system with a Hamiltonian given...
Problem 8.3 - A New Two-State System Consider a new two-level system with a Hamiltonian given by i = Ti 1461 – 12) (2) (3) Also consider an observable represented by the operator Ŝ = * 11/21 - *12/11: It should (hopefully) be clear that 1) and 2) are eigenkets of the Hamiltonian. Let $1) be an eigenket of S corresponding to the smaller eigenvalue of S and let S2) be an eigenket of S corresponding to the larger eigenvalue....
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...
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...
Find the eigenvalue of the total spin angular momentum operator, s^2. 2) Find the eigenvalue of...
Find the eigenvalue of the total spin angular momentum
operator, s^2.
2) Find the eigenvalue of the total spin angular momentum operator, $2.
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?...
Problem2 Two possible wave functions for two spin 1 /2 particles with Sz = 0 are Apply the operator S+ to both states as many times as needed to find the largest possible value for m and hence det...
Problem2 Two possible wave functions for two spin 1 /2 particles with Sz = 0 are Apply the operator S+ to both states as many times as needed to find the largest possible value for m and hence determine the value of S2 for each state
Problem2 Two possible wave functions for two spin 1 /2 particles with Sz = 0 are Apply the operator S+ to both states as many times as needed to find the largest possible value...
Consider a three-level system where the Hamiltonian and
observable A are given by the matrix Aˆ = µ 0 1 0 1 0 1 0 1 0
Hˆ = ¯hω 1 0 0 0 1 0 0 0 1 (a) What are the possible
values obtained in a measurement of A (b) Does a state exist in
which both the results of a measurement of energy E and observable
A can be...
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...
[3] A spin-1/2 particle is in the state IW) 1/311) +i2/3|). (a) A measurement is made of the x component of the spin. What is the probability that the spin will be in the +z direction? (b) Suppose a measurement is made of the spin in the z direction and it is found that the particle has m,#1/2. what is the state after the measurement? (c) Now a second measurement is made immediately after to determine the spin in the...
Consider the state of a spin-1/2 particle 14) = v1o (31+z) + i] – z)) where | z) are the eigenstates of the operator of the spin z-component $z. 1. Show that [V) is properly normalized, i.e. (W14) = 1. 2. Calculate the probability that a measurement of $x = 6x yields 3. Calculate the expectation value (Šx) for the state 14) and its dispersion ASx = V(@z) – ($()2. 4. Assume that the spin is placed in the magnetic...
Problem 8.3 - A New Two-State System Consider a new two-level system with a Hamiltonian given by i = Ti 1461 – 12) (2) (3) Also consider an observable represented by the operator Ŝ = * 11/21 - *12/11: It should (hopefully) be clear that 1) and 2) are eigenkets of the Hamiltonian. Let $1) be an eigenket of S corresponding to the smaller eigenvalue of S and let S2) be an eigenket of S corresponding to the larger eigenvalue....
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...
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...
Find the eigenvalue of the total spin angular momentum
operator, s^2.
2) Find the eigenvalue of the total spin angular momentum operator, $2.
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?...
Problem2 Two possible wave functions for two spin 1 /2 particles with Sz = 0 are Apply the operator S+ to both states as many times as needed to find the largest possible value for m and hence determine the value of S2 for each state
Problem2 Two possible wave functions for two spin 1 /2 particles with Sz = 0 are Apply the operator S+ to both states as many times as needed to find the largest possible value...
Most questions answered within 3 hours.
-
if 14.3 g of table salt (nacl) is put into 236.0 g of water at
25...
asked 48 minutes ago -
Free content. Free software. Freemium pricing models. Viral
popularity. Disappearing gatekeepers. These are the disrupters of...
asked 2 hours ago -
Consider the simple linear regression model: HARD1 =
β0 + β1*SCORE + є, where
є ~...
asked 3 hours ago -
In the Chesapeake region during the mid-17th
century how similar was the experience of an independent...
asked 5 hours ago -
. A 2.50 M stock solution was used to prepare a dilute NaOH
solution with a...
asked 6 hours ago -
Write a program that reads in a text file, infile.txt, and
prints out all the lines...
asked 8 hours ago -
Which of the following orbits have a total of zero energy (based
on the common convention)?...
asked 9 hours ago -
Find the expected count and the contribution to the chi-square
statistic for the (Group 1, No)...
asked 10 hours ago -
Suppose you are purchasing a meal and with every meal a you
receive one of 10...
asked 10 hours ago -
A 75.0 kg 0erson is riding in a car moving at 20.0 m/s when the
car...
asked 10 hours ago -
What does Δp = QR mean in words?
Pushing a viscous fluid through a pipe requires...
asked 10 hours ago -
We know that system.out.println (“object number” + n ); is
legal.String name; int n; name =...
asked 10 hours ago