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[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...
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...
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...
3. (6 points) Measurements on a two-particle state Consider the state for a system of two...
3. (6 points) Measurements on a two-particle state Consider the state for a system of two spin-1/2 particles, (2]+).I+)2 +1-)[+)2-1-)1-)2). (a) Show that this state is normalized. (b) What is the probability of measuring S: (the z-component of spin for particle 1) to be +h/2? After this measurement is made with this result, what is the state of the system? If we make a measurement in this new state, what is now the probability of measuring S3 = +h/2? (e)...
4. Spin (10 marks) Suppose an electron is in a state such that its spin can...
4. Spin (10 marks) Suppose an electron is in a state such that its spin can be described by a linear superposition of the eigenspinors of S +A 32 2/22 (a) Normalise the state. (b) What are the possible outcomes of a measurement of the z-component of the spin? What is the probability of each possible result? (c) What are the expectation value and uncertainty of the z-component of the spin? (d) What are the possible results of measuring the...
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...
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...
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...
Please show details steps and explanation, label each part ,thank you very much! a) b) Consider the normalized state for a quantum mechanical particle of mass μ con- strained to move on a circle of...
Please show details steps and explanation, label each
part ,thank you very much!
a)
b)
Consider the normalized state for a quantum mechanical particle of mass μ con- strained to move on a circle of radius ro, given by: If you measured the z-component of angular momentum to be 3h, what would the state of the particle be immediately after the measurement is made? If you measured the z-component of angular momentum at some time tメ0, what is the probability...
(2.1) (20 points) A spin 1/2 particle is in an eigenstate of Sy with eigenvalue h/2...
(2.1) (20 points) A spin 1/2 particle is in an eigenstate of Sy with eigenvalue h/2 at the initial time t = 0. At that time, it is placed in a magnetic induction B = B2, and it is then allowed to precess in that induction for the time T. Then, at that instant T, B is instantaneously rotated from the z to the y direction, becoming B = Bį. After another identical time interval T occurs, a measurement of...
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.
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...
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...
3. (6 points) Measurements on a two-particle state Consider the state for a system of two spin-1/2 particles, (2]+).I+)2 +1-)[+)2-1-)1-)2). (a) Show that this state is normalized. (b) What is the probability of measuring S: (the z-component of spin for particle 1) to be +h/2? After this measurement is made with this result, what is the state of the system? If we make a measurement in this new state, what is now the probability of measuring S3 = +h/2? (e)...
4. Spin (10 marks) Suppose an electron is in a state such that its spin can be described by a linear superposition of the eigenspinors of S +A 32 2/22 (a) Normalise the state. (b) What are the possible outcomes of a measurement of the z-component of the spin? What is the probability of each possible result? (c) What are the expectation value and uncertainty of the z-component of the spin? (d) What are the possible results of measuring the...
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...
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...
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...
Please show details steps and explanation, label each
part ,thank you very much!
a)
b)
Consider the normalized state for a quantum mechanical particle of mass μ con- strained to move on a circle of radius ro, given by: If you measured the z-component of angular momentum to be 3h, what would the state of the particle be immediately after the measurement is made? If you measured the z-component of angular momentum at some time tメ0, what is the probability...
(2.1) (20 points) A spin 1/2 particle is in an eigenstate of Sy with eigenvalue h/2 at the initial time t = 0. At that time, it is placed in a magnetic induction B = B2, and it is then allowed to precess in that induction for the time T. Then, at that instant T, B is instantaneously rotated from the z to the y direction, becoming B = Bį. After another identical time interval T occurs, a measurement of...
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