3. What is the conductance of a quantum point contact large enough to allow three states...
3. What is the conductance of a quantum point contact large enough to allow three states in the constriction region? (3 points)
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3. What is the conductance of a quantum point contact large
enough to allow three states...
6. Consider a quantum system of N particles with only three possible states to oc- cupy...
6. Consider a quantum system of N particles with only three possible states to oc- cupy for each particle. The energy values of these states are equal to 0, €and €3, respectively. (a) [10 points) You observe that the probability to sample eash state is P = 0.9. P2 = 0.09 and p = 0.01 at T = 300 K. What are the energies and c? Recall that the probability to occupy state is proportional to where k= 1.38 x...
6. Consider a quantum system of N particles with only three possible states to oc cupy...
6. Consider a quantum system of N particles with only three possible states to oc cupy for each particle. The energy values of these states are equal to 0, E and 3, respectively. (a) (10 points) You observe that the probability to sample eash state is p=0.9, P2 = 0.09 and p = 0.01 at T = 300 K. What are the energies ez and ez? Recall that the probability to occupy 4th state is proportional to e«/T where k...
Problem 1. Consider a system of three identical particles. Each particle has 5 quantum states with...
Problem 1. Consider a system of three identical particles. Each particle has 5 quantum states with energies 0, ε, 2E, 3E, 4E. For distinguishable particles, calculate the number of quantum states where (1) three particles are in the same single-particle state, (2) only two particles are in the same single-particle state, and (3) no two particles are in the same single-particle state. Problem 2. For fermions, (1) calculate the total number of quantum states, and (2) the number of states...
3.3 One spin in thermal contact with a large spin system Generalize the preceding problem by...
3.3 One spin in thermal contact with a large spin system Generalize the preceding problem by considering the case where the system A' consists of some arbitrarily large number N of spins J, each having magnetic moment plo. The system A consists again of a single spin { with mag- netic moment Mo. Both A and A' are located in the same magnetic field B and are placed in contact with each other so that they are free to exchange...
2. Probabilities and Phases: Consider the following three quantum states that are a normalised su- perposition of the b...
2. Probabilities and Phases: Consider the following three quantum states that are a normalised su- perposition of the basis states, | ). -), associated with the measurement of the S, observable Calculate the probabilities for the respective results of Stern-Gerlach measurements performed on each state in each of the three orthogonal directions, t, and Summarising your results in a 3 x 6 table, what do you learn about the importance for computing probabilities of the global phase (in this case,...
HW12.2 (3 points) [1,1],[1,0),[1,-1) are the three eigenstates of Lạ& Ly with quantum number l =...
HW12.2 (3 points) [1,1],[1,0),[1,-1) are the three eigenstates of Lạ& Ly with quantum number l = 1 and m = 1,0,-1, respectively. a) (1 point) What are the following states Lx|1,1) =? Lx|1,0) = ? Lx|1, -1) = ? b) (1 point) Find out eigenstates of Lx that are linear combinations of (1,1),(1,0), and (1,-1) What is the corresponding eigenvalue for each of the eigenstate you find? c) (1 point) What is the matrix representation of Lx in the basis...
As discussed in class, what characteristic of Venezuelan oil demands large levels of investment to allow...
As discussed in class, what characteristic of Venezuelan oil demands large levels of investment to allow it to be transmitted from wellhead to others points (like tankers). Lack of such investment has caused oil production to be significantly curtailed. (1 point) 5)
E8C.6(a) An electron in tu and 1. What is its orbital E8C.6(b) What are the allow...
E8C.6(a) An electron in tu and 1. What is its orbital E8C.6(b) What are the allow ectron in two different states of an atom is known to have i = its orbital angular momentum quantum number in each case? What are the allowed total angular momentum quantum numbers of composite system in which j = 5 and j, = 3?
What does a large Keq value mean? (1 point) a Tendency to not obtain enough products...
What does a large Keq value mean? (1 point) a Tendency to not obtain enough products in a reaction. b Tendency to decrease the entropy in the system. c Tendency of a reaction to proceed until all reactants turn into products.
3 Problem Three [10 points] (The Quantum Oscillator) We have seen in class that the Hamiltonian...
3 Problem Three [10 points] (The Quantum Oscillator) We have seen in class that the Hamiltonian of a particle of a simple Harmonic oscillator potential in one dimension can be expressed in term of the creation and annihilation operators àt and à, respectively, as: or with In >, n = 0,1,..) are the nth eigenstates of the above Hamiltonian. Part A A.1. Show that the energy levels of a simple harmonic oscillator are E,' Aw (nti), n=0, 12, A.2. Calculate...
6. Consider a quantum system of N particles with only three possible states to oc- cupy for each particle. The energy values of these states are equal to 0, €and €3, respectively. (a) [10 points) You observe that the probability to sample eash state is P = 0.9. P2 = 0.09 and p = 0.01 at T = 300 K. What are the energies and c? Recall that the probability to occupy state is proportional to where k= 1.38 x...
6. Consider a quantum system of N particles with only three possible states to oc cupy for each particle. The energy values of these states are equal to 0, E and 3, respectively. (a) (10 points) You observe that the probability to sample eash state is p=0.9, P2 = 0.09 and p = 0.01 at T = 300 K. What are the energies ez and ez? Recall that the probability to occupy 4th state is proportional to e«/T where k...
Problem 1. Consider a system of three identical particles. Each particle has 5 quantum states with energies 0, ε, 2E, 3E, 4E. For distinguishable particles, calculate the number of quantum states where (1) three particles are in the same single-particle state, (2) only two particles are in the same single-particle state, and (3) no two particles are in the same single-particle state. Problem 2. For fermions, (1) calculate the total number of quantum states, and (2) the number of states...
3.3 One spin in thermal contact with a large spin system Generalize the preceding problem by considering the case where the system A' consists of some arbitrarily large number N of spins J, each having magnetic moment plo. The system A consists again of a single spin { with mag- netic moment Mo. Both A and A' are located in the same magnetic field B and are placed in contact with each other so that they are free to exchange...
2. Probabilities and Phases: Consider the following three quantum states that are a normalised su- perposition of the basis states, | ). -), associated with the measurement of the S, observable Calculate the probabilities for the respective results of Stern-Gerlach measurements performed on each state in each of the three orthogonal directions, t, and Summarising your results in a 3 x 6 table, what do you learn about the importance for computing probabilities of the global phase (in this case,...
HW12.2 (3 points) [1,1],[1,0),[1,-1) are the three eigenstates of Lạ& Ly with quantum number l = 1 and m = 1,0,-1, respectively. a) (1 point) What are the following states Lx|1,1) =? Lx|1,0) = ? Lx|1, -1) = ? b) (1 point) Find out eigenstates of Lx that are linear combinations of (1,1),(1,0), and (1,-1) What is the corresponding eigenvalue for each of the eigenstate you find? c) (1 point) What is the matrix representation of Lx in the basis...
As discussed in class, what characteristic of Venezuelan oil demands large levels of investment to allow it to be transmitted from wellhead to others points (like tankers). Lack of such investment has caused oil production to be significantly curtailed. (1 point) 5)
E8C.6(a) An electron in tu and 1. What is its orbital E8C.6(b) What are the allow ectron in two different states of an atom is known to have i = its orbital angular momentum quantum number in each case? What are the allowed total angular momentum quantum numbers of composite system in which j = 5 and j, = 3?
3 Problem Three [10 points] (The Quantum Oscillator) We have seen in class that the Hamiltonian of a particle of a simple Harmonic oscillator potential in one dimension can be expressed in term of the creation and annihilation operators àt and à, respectively, as: or with In >, n = 0,1,..) are the nth eigenstates of the above Hamiltonian. Part A A.1. Show that the energy levels of a simple harmonic oscillator are E,' Aw (nti), n=0, 12, A.2. Calculate...
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