Homework Answers
![Putring ruese values in see that [Sz &] to. of spin (st) and ů are measurable. equation ③ we Henced z-compment not simultaneo](http://img.homeworklib.com/questions/d81cf250-2d51-11ec-b17a-6fd746c85546.png?x-oss-process=image/resize,w_560)
Add Answer to:
2. Consider a spin-1/2 particle. The physical quantity K is represented by the operator (written in...
[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...
2. Spin-1/2 system: (20 points) The Pauli matrices are, 0 -1 from which we can define...
2. Spin-1/2 system: (20 points) The Pauli matrices are, 0 -1 from which we can define the spin matrices, s.-슬&z, Šv = , S.-출.. We'll use the eigenkets of S that, for the spin half system, they can be represented by the spinors, a) Show, by matrix multiplication that |+) and |-) are eigenstates of the S operator and determine the eigenvalues. Show that they are not eigenstates of S and Sy b) Show that the matrix squares s ,...
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...
A spin-1 particle interacts with an external magnetic field B = B. The interaction Hamiltonian for the system is H = gB-S, where S-Si + Sỳ + SE is the spin operator. (Ignore all degrees of freedom ot...
A spin-1 particle interacts with an external magnetic field B = B. The interaction Hamiltonian for the system is H = gB-S, where S-Si + Sỳ + SE is the spin operator. (Ignore all degrees of freedom other than spin.) (a) Find the spin matrices in the basis of the S. S eigenstates, |s, m)) . (Hint: Use the ladder operators, S -S, iS, and S_-S-iS,, and show first that s_ | 1,0-ћ /2 | 1.-1)) . Then use these...
3. (a) A particle orbits a fixed point in space. Given that L-=-ih- , find the...
3. (a) A particle orbits a fixed point in space. Given that L-=-ih- , find the eigenvalues аф and normalised eigenfunctions of the z-component of the particle's angular momentum. (5 marks) Explain clearly your reasoning at each important step An electron is in the spin state x)-A G) Normalise x) and hence determine the constant A (ii) If you measured the z-component of the electron's spin, s, . what values could (b) in the usual s basis you get and...
Incorrect Question 9 0/1 pts The state % = to 4-1 + tzv. + tag 42...
Incorrect Question 9 0/1 pts The state % = to 4-1 + tzv. + tag 42 is a linear combination of three orthonormal eigenstates of the operator Ô corresponding to eigenvalues - 1, 1, and 2. What is the expectation value for Ô for this state? V o 13+2821 Which of the following is true of observable in quantum mechanics? I. They are represented by Hermitian operators. II. Multiple observables can never be simultaneously measured. III. The operators representing observables...
(L43*) Spin can be represented by matrices. Show that all three spin matrices l 0 2 0 -1 0),"2=2 1 have eigenval...
(L43*) Spin can be represented by matrices. Show that all three spin matrices l 0 2 0 -1 0),"2=2 1 have eigenvalues of +1/2h and -1/2h. Calculate the corresponding eigenfunctions which we will denote as α-and β-eigenfunctions corresponding to spin l/2 particles. Show that Sj can be determined by the commutation of the other two matrices sn and sm, n, maj. Prove that the (2×2) matrix sz-s' +ss+s, commutes with all spin matrices, ie. s2s,-sis-. Calculate the eigenvalues of s2....
4. 10 points The Spin operators for a spin-1/2 particle can be described by the Pauli...
4. 10 points The Spin operators for a spin-1/2 particle can be described by the Pauli matrices: 0 1 0 0 ,02= 0 -1 1 ¿ a) Write the normalized eigenvectors of Oz, I+) and 1-) which are defined such that 0z|+) = 1+) and 0z1-) = -1-), as column vectors in the same basis as the Pauli matrices given above. (You can assume without loss of generality that these eigenvectors are real.) (3 pts) b) Consider an eigenvector (V)...
2. Addition of Angular Momentum a) (8pts) Given two spin 1/2 particles, what are the four possibilities for their spin configuration? Put your answer in terms of states such as | 11). where the f...
2. Addition of Angular Momentum a) (8pts) Given two spin 1/2 particles, what are the four possibilities for their spin configuration? Put your answer in terms of states such as | 11). where the first arrow denotes the z-component of the particle's spin. Identify the m values for each state. b)(7pts) If you apply the lowering operator to a state you get Apply the two-state lowering operator S--S(,) +S(), where sti) acts on the first state and S acts on...
Two particle state
Two Particle State problem, measurement of total angular momentum, finding probabilities, action of lowering operatora) A particle of spin \(3 / 2\) and a particle of spin 1 are found in the state \(\left|\frac{3}{2}-\frac{1}{2}\right\rangle\) of total spin. Assume that the particles are in a state of zero orbital angular momentum.Find which values of the z-component of the spin of the two particles can be measured and with what probabilities.The following information applies to parts \(\mathbf{b}\) ) and \(\mathbf{c}\) ).An electron...
[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...
2. Spin-1/2 system: (20 points) The Pauli matrices are, 0 -1 from which we can define the spin matrices, s.-슬&z, Šv = , S.-출.. We'll use the eigenkets of S that, for the spin half system, they can be represented by the spinors, a) Show, by matrix multiplication that |+) and |-) are eigenstates of the S operator and determine the eigenvalues. Show that they are not eigenstates of S and Sy b) Show that the matrix squares s ,...
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...
A spin-1 particle interacts with an external magnetic field B = B. The interaction Hamiltonian for the system is H = gB-S, where S-Si + Sỳ + SE is the spin operator. (Ignore all degrees of freedom other than spin.) (a) Find the spin matrices in the basis of the S. S eigenstates, |s, m)) . (Hint: Use the ladder operators, S -S, iS, and S_-S-iS,, and show first that s_ | 1,0-ћ /2 | 1.-1)) . Then use these...
3. (a) A particle orbits a fixed point in space. Given that L-=-ih- , find the eigenvalues аф and normalised eigenfunctions of the z-component of the particle's angular momentum. (5 marks) Explain clearly your reasoning at each important step An electron is in the spin state x)-A G) Normalise x) and hence determine the constant A (ii) If you measured the z-component of the electron's spin, s, . what values could (b) in the usual s basis you get and...
Incorrect Question 9 0/1 pts The state % = to 4-1 + tzv. + tag 42 is a linear combination of three orthonormal eigenstates of the operator Ô corresponding to eigenvalues - 1, 1, and 2. What is the expectation value for Ô for this state? V o 13+2821 Which of the following is true of observable in quantum mechanics? I. They are represented by Hermitian operators. II. Multiple observables can never be simultaneously measured. III. The operators representing observables...
(L43*) Spin can be represented by matrices. Show that all three spin matrices l 0 2 0 -1 0),"2=2 1 have eigenvalues of +1/2h and -1/2h. Calculate the corresponding eigenfunctions which we will denote as α-and β-eigenfunctions corresponding to spin l/2 particles. Show that Sj can be determined by the commutation of the other two matrices sn and sm, n, maj. Prove that the (2×2) matrix sz-s' +ss+s, commutes with all spin matrices, ie. s2s,-sis-. Calculate the eigenvalues of s2....
4. 10 points The Spin operators for a spin-1/2 particle can be described by the Pauli matrices: 0 1 0 0 ,02= 0 -1 1 ¿ a) Write the normalized eigenvectors of Oz, I+) and 1-) which are defined such that 0z|+) = 1+) and 0z1-) = -1-), as column vectors in the same basis as the Pauli matrices given above. (You can assume without loss of generality that these eigenvectors are real.) (3 pts) b) Consider an eigenvector (V)...
2. Addition of Angular Momentum a) (8pts) Given two spin 1/2 particles, what are the four possibilities for their spin configuration? Put your answer in terms of states such as | 11). where the first arrow denotes the z-component of the particle's spin. Identify the m values for each state. b)(7pts) If you apply the lowering operator to a state you get Apply the two-state lowering operator S--S(,) +S(), where sti) acts on the first state and S acts on...
Most questions answered within 3 hours.
-
A regression equation that describes the relationship between
the amount of the bill ($) at a...
asked 38 minutes ago -
exercise on VSEPR and molecular structrue.
octahedral
SeCl62-
TeCl62-
ClF62-
distorted
SeF62–
IF6–
asked 1 hour ago -
284 mL of a 0.52 M potassium hydroxide solution is added to 467
mL of a...
asked 1 hour ago -
Little’s Law: Val d’Costa is a world famous ski village in the
French Alps. Because of...
asked 1 hour ago -
Find the absolute error D for the calculation if A + B/C=D A=
9.4 +/- 0.4...
asked 2 hours ago -
New Air Heating and Cooling, manufactures furnaces and central
air units. The company pride itself on...
asked 2 hours ago -
A coach uses a new technique to train gymnasts. Seven
gymnasts were randomly selected and their...
asked 4 hours ago -
While rotating the tires on your car you notice a rock [mass =
0.1 Kg] stuck...
asked 6 hours ago -
Using MARS simulator, write MIPS programs according to
the following scenarios: Receive a positive integer number...
asked 8 hours ago -
An object in front of a concave mirror has a real image that is
11.5 cm...
asked 8 hours ago -
Consider the reaction, C3 H8 + O2 --> CO2 + H2O. How many
moles of O2...
asked 10 hours ago -
You and your opponent both roll a fair die. If you both roll the
same number,...
asked 10 hours ago