Homework Answers
Add Answer to:
The spin operator along an arbitrary direction = (sin 0 cos 0) is defined as sin...
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 ,...
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...
A. In class we found the eigenstate for spin along an arbitrary direction n-sinBcospa + s1ηθsinqy...
A. In class we found the eigenstate for spin along an arbitrary direction n-sinBcospa + s1ηθsinqy + coseż. This state could be represented as CeVsin(θ/2 te could be represented as (cosC0/2) For this state, find the probabilities for measuring the following: sz+h/2, sz--h/2, sx -
2. Consider a spin-1/2 particle. The physical quantity K is represented by the operator (written in...
2. Consider a spin-1/2 particle. The physical quantity K is represented by the operator (written in the S-basis): k=ko –2i) * +2i 0 where k is a real number with the appropriate dimensions. (a) What are the eigenvalues and normalized eigenstates of K? (b) What value(s) of K could you measure? (c) What state(s) could the particle be in immediately after you measured K? (d) For a single particle, could you simultaneously know both the z-component of spin and the...
For the case with spin , prove that U(Rn(a)) = e-inga for arbitrary axis parameterized by...
For the case with spin , prove that U(Rn(a)) = e-inga for arbitrary axis parameterized by ñ = sin cos oi+sin sin oj+cos ek, where Ô = (0,0,0%) are the three Pauli matrices. • Then show that the rotational operator has the following explicit form U(R(Q)) = cos 1 – i sin añoở. You may Taylor expand the exponential operator to find the explicit form.
2- If the z-component of an electron spin is +h/2, what is the probability that its component along a direction z', that forms an angle θ with the z-axis, equals +h/2 or-h/2? What is the avera...
2- If the z-component of an electron spin is +h/2, what is the probability that its component along a direction z', that forms an angle θ with the z-axis, equals +h/2 or-h/2? What is the average value of the spin along z'? (Hint. Sz.-S. n where n; sin θ cospi + sin θ sin φ j + cos θ k is a unit vector along z'.) (10 Scores)
2- If the z-component of an electron spin is +h/2, what is...
Problem 2. (30 points) The spin states: s 1,m) and Is -2, m1) composed of spin-3/2 and spin-1/2 states are linear combi...
Problem 2. (30 points) The spin states: s 1,m) and Is -2, m1) composed of spin-3/2 and spin-1/2 states are linear combinations of s1 3/2,m-3/2;2 1/2,m2 1/2) and 81-3/2, m-1/2; 2 1/2, m2--1/2), that is 11.-1)-cos θ3/2,-3/2; 1/2, 1/2) _ sin θ|3/2.-1/2; 1/2,-1/2), 2.-1) sin θ|3/2,-3/2; 1/2, 1/2) + cos θ|3/2.-1/2: 1/2,-1/2) a) Determine the values for cos θ and sin θ b) Express |3/2,-3/2; 1/2, 1/2) and |3/2,-1/2;1/2,-1/2) as functions of |1, -1) and 2,-1) c) A system of...
Consider an electron in a uniform magnetic field along the z direction. A measurement shows that...
Consider an electron in a uniform magnetic field along the z direction. A measurement shows that the spin is along the negative x direction at -0. a. Find the eigenvector describing the initial spin state. 5. 0 -1 b. Write the Hamiltonian as a 2x2 matrix by starting with H =-7S-Band taking the field B in the z- direction. Find the energy eigenvalues and eigenvectors. Solve for | Ψ(t) using these eigenvalues, eigenvectors, and the initial condition from part a....
1. Show y = sin ax is not an eigenfunction of the operator d/dx, but is...
1. Show y = sin ax is not an eigenfunction of the operator d/dx, but is an eigenfunction of the operator da/dx. 2. Show that the function 0 = Aeimo , where i, m, and A are constants, is an eigenfunction of the angular momentum operator is the z-direction: M =; 2i ap' and what are the eigenvalues? 3. Show the the function y = Jź sin MA where n and L are constants, is an eigenfunction of the Hamiltonian...
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.
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 ,...
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...
A. In class we found the eigenstate for spin along an arbitrary direction n-sinBcospa + s1ηθsinqy + coseż. This state could be represented as CeVsin(θ/2 te could be represented as (cosC0/2) For this state, find the probabilities for measuring the following: sz+h/2, sz--h/2, sx -
2. Consider a spin-1/2 particle. The physical quantity K is represented by the operator (written in the S-basis): k=ko –2i) * +2i 0 where k is a real number with the appropriate dimensions. (a) What are the eigenvalues and normalized eigenstates of K? (b) What value(s) of K could you measure? (c) What state(s) could the particle be in immediately after you measured K? (d) For a single particle, could you simultaneously know both the z-component of spin and the...
For the case with spin , prove that U(Rn(a)) = e-inga for arbitrary axis parameterized by ñ = sin cos oi+sin sin oj+cos ek, where Ô = (0,0,0%) are the three Pauli matrices. • Then show that the rotational operator has the following explicit form U(R(Q)) = cos 1 – i sin añoở. You may Taylor expand the exponential operator to find the explicit form.
2- If the z-component of an electron spin is +h/2, what is the probability that its component along a direction z', that forms an angle θ with the z-axis, equals +h/2 or-h/2? What is the average value of the spin along z'? (Hint. Sz.-S. n where n; sin θ cospi + sin θ sin φ j + cos θ k is a unit vector along z'.) (10 Scores)
2- If the z-component of an electron spin is +h/2, what is...
Problem 2. (30 points) The spin states: s 1,m) and Is -2, m1) composed of spin-3/2 and spin-1/2 states are linear combinations of s1 3/2,m-3/2;2 1/2,m2 1/2) and 81-3/2, m-1/2; 2 1/2, m2--1/2), that is 11.-1)-cos θ3/2,-3/2; 1/2, 1/2) _ sin θ|3/2.-1/2; 1/2,-1/2), 2.-1) sin θ|3/2,-3/2; 1/2, 1/2) + cos θ|3/2.-1/2: 1/2,-1/2) a) Determine the values for cos θ and sin θ b) Express |3/2,-3/2; 1/2, 1/2) and |3/2,-1/2;1/2,-1/2) as functions of |1, -1) and 2,-1) c) A system of...
Consider an electron in a uniform magnetic field along the z direction. A measurement shows that the spin is along the negative x direction at -0. a. Find the eigenvector describing the initial spin state. 5. 0 -1 b. Write the Hamiltonian as a 2x2 matrix by starting with H =-7S-Band taking the field B in the z- direction. Find the energy eigenvalues and eigenvectors. Solve for | Ψ(t) using these eigenvalues, eigenvectors, and the initial condition from part a....
1. Show y = sin ax is not an eigenfunction of the operator d/dx, but is an eigenfunction of the operator da/dx. 2. Show that the function 0 = Aeimo , where i, m, and A are constants, is an eigenfunction of the angular momentum operator is the z-direction: M =; 2i ap' and what are the eigenvalues? 3. Show the the function y = Jź sin MA where n and L are constants, is an eigenfunction of the Hamiltonian...
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.
Most questions answered within 3 hours.
-
Why
are large,multinational firms more likely to be concerned about
CSR?Why are lifestyle brands more susceptible...
asked 3 minutes ago -
answer the below qestion in term of marketing in “personal
selling steps”
( Question )
Consider...
asked 4 minutes ago -
Under normal use conditions, the Mean Time To Failure of a
heating coil can be modeled...
asked 5 minutes ago -
A student holds a ruler by one end (x=0 where the student holds
it). The student...
asked 5 minutes ago -
People are most likely to believe their ancestors play an active
role in their lives in...
asked 6 minutes ago -
A speeding car is traveling along a straight road with a
constant speed of 100 km/hour....
asked 23 minutes ago -
When 60.1 gg of calcium is reacted with nitrogen gas, 31.7 gg of
calcium nitride is...
asked 28 minutes ago -
The random variable X is exponentially distributed, where X
represents the time it takes for a...
asked 43 minutes ago -
a) Write a verilog module for 1:4 Demultiplexer using verilog
primitives.
b) Design 1-to-4 DEMUX using...
asked 38 minutes ago -
MATLAB
write a MATLAB function (1) output a third-order polynomial
function with the coefficients as the...
asked 51 minutes ago -
A z-score
communicates a raw score’s "relative standing"
under the normal curve in relation to:
asked 59 minutes ago -
An object is vibrating on a spring with the following equation
of motion:
?=(30 ??)cos((2?)/(160)?)
a)...
asked 58 minutes ago