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1 2. Consider the normalized spin state To (31t) +i\L)) (2) 10 (a) Is this state...
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...
1. An angular momentum system is prepared in the state, )I,1)V0) +i12,2)-12,0) a) What are the...
1. An angular momentum system is prepared in the state, )I,1)V0) +i12,2)-12,0) a) What are the possible measurements of L2, and what are their probabilities? b) What are the possible results of a measurement of the z-component of angular momentum, and their probabilities? c) Explain why this preparation is not a possible spin angular momentum state.
A zero-spin particle with angular m0mentum quantum numbers l=1and m=1 passes though a Stern Gerlach apparatus...
A zero-spin particle with angular m0mentum quantum numbers l=1and m=1 passes though a Stern Gerlach apparatus oriented so as to measure Lx, what possible results could be obtained and what are their relative probabilities? In each case, describe the form of the angular part of the wavefunction following the measurement.
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...
Question #2: 6 pts] Find the eigenvalues and the normalized eigenvectors of the matrix 21 2...
Question #2: 6 pts] Find the eigenvalues and the normalized eigenvectors of the matrix 21 2 -1 2 Question #3: 10 pts] The electron in a hydrogen atom is a linear combination of eigenstates. Let us assume a limited linear combination to provide some sample calculations $(r, θ, φ) 2 ,1,0,0 + '2,1,0 (a) Normalize the above equation. (b) What are the possible results of individual measurements of energy, angular momentum, and the z-component of angular momentum? (c) What are...
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...
(V.4) A particle is observed to have orbital angular momentum quantum number 2. The z component...
(V.4) A particle is observed to have orbital angular momentum quantum number 2. The z component of the angular momentum is measured to be Lz2h. A second particle is observed to have orbital angular momentum quantum number l2-2 and a z component ha = +2 V1(1 +1), what are the possible outcomes, and with what relative probabilities? What is the expectation value (L)'? h. If a measurement is made of the total angular momentum L-h
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)...
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...
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...
1. An angular momentum system is prepared in the state, )I,1)V0) +i12,2)-12,0) a) What are the possible measurements of L2, and what are their probabilities? b) What are the possible results of a measurement of the z-component of angular momentum, and their probabilities? c) Explain why this preparation is not a possible spin angular momentum state.
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...
Question #2: 6 pts] Find the eigenvalues and the normalized eigenvectors of the matrix 21 2 -1 2 Question #3: 10 pts] The electron in a hydrogen atom is a linear combination of eigenstates. Let us assume a limited linear combination to provide some sample calculations $(r, θ, φ) 2 ,1,0,0 + '2,1,0 (a) Normalize the above equation. (b) What are the possible results of individual measurements of energy, angular momentum, and the z-component of angular momentum? (c) What are...
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...
(V.4) A particle is observed to have orbital angular momentum quantum number 2. The z component of the angular momentum is measured to be Lz2h. A second particle is observed to have orbital angular momentum quantum number l2-2 and a z component ha = +2 V1(1 +1), what are the possible outcomes, and with what relative probabilities? What is the expectation value (L)'? h. If a measurement is made of the total angular momentum L-h
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)...
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...
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