2. Let T the temperature of system A in problem 1. 3 as in problem 1 (a) is T 0 orT
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1. System A is comprised of 2 electrons,it interacts with system A' which is comprised of 3 elect...
Problem 111.3. A spin 1/2 particle interacts with a nnagnetic field B = Boe through the...
Problem 111.3. A spin 1/2 particle interacts with a nnagnetic field B = Boe through the Pauli interaction H-μσ. B where μ is the magnetic moment. The Pauli spin matrices are İ-(Oz,@yMwwhere the σί are T0 1 0-il The eigenstates for d, are the spinors 0 (a) (3 pts.) Suppose that at time t-0 the particle is in an eigenstate Xx corresponding to spin pointing along the positive z-axis. Find the eigenstatexz in terms of α and β. (b) (7...
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...
1. Consider a quantum system comprising three indistinguishable particles which can occupy only three individual-partic...
1. Consider a quantum system comprising three indistinguishable particles which can occupy only three individual-particle energy levels, with energies ε,-0, ε,-2e and ε,-3. The system is in thermal equilibrium at temperature T. Suppose the particles are bosons with integer spin. i) How many states do you expect this system to have? Justify your answer [2 marks] (ii) Make a table showing, for each state of this system, the energy of the state, the number of particles (M, M,, N) with...
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...
3.3 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...
Match the following correctly principal quantum number, n=12.3 Al=0, 1, 2, 3, 4 B. designates siz...
Match the following correctly principal quantum number, n=12.3 Al=0, 1, 2, 3, 4 B. designates size and energy C. s and p electrons outside noble gas or angular momentum quantum number, l-0 to (n-1) pseudo-noble gas core, involved in chemical reactions , p, d, f, g-which numbers? magnetic quantum number, m,--l to+1 spin quantum number m s=+1/2 or-1/2 Pauli Exclusion principle Aufbau Principle Hund's Rule pseudo-noble gas core D, no 2 electrons in an atom have the same 4 quantum...
Try to avoid handwriting please, thank you. 1. Consider the gas of electrons in gold, as...
Try to avoid handwriting please, thank you.
1. Consider the gas of electrons in gold, as in problem 3 above. (a) Begin by assuming the gas obeys classical statistics. Using the Som- merfeld model for the density of states, an analysis shows that the partition function in the MB distribution is given by (where V is the volume) m3/2v Plug this into the MB distribution and plot N(E) as a function of E. Assume a temperature T 300 K and...
Match the following correctly principal quantum number, n=12.3 Al=0, 1, 2, 3, 4 B. designates size...
Match the following correctly principal quantum number, n=12.3 Al=0, 1, 2, 3, 4 B. designates size and energy C. s and p electrons outside noble gas or angular momentum quantum number, l-0 to (n-1) pseudo-noble gas core, involved in chemical reactions , p, d, f, g-which numbers? magnetic quantum number, m,--l to+1 spin quantum number m s=+1/2 or-1/2 Pauli Exclusion principle Aufbau Principle Hund's Rule pseudo-noble gas core D, no 2 electrons in an atom have the same 4 quantum...
signals and systems Question 1 (30%): Consider a LTI systern which is comprised of four subsystems...
signals and systems
Question 1 (30%): Consider a LTI systern which is comprised of four subsystems whose impulse responses are hi(t), h2(t). ha(t), and ha(t). u(t) f(t) hi(t) h2(t) 13 ha(1) Where: hi (t) = δ(t + 1) h2(t) = 2(u(t)-u(t-1)] hs(t) = 201t-2) h1(t) = u(t + 2)-u(t) a) (8%) Compute the overall impulse response htotal(t) of the system comprised of hi(t), h2(t), hs(t), and h4(t). Sketch and write the expression for htotai(t) b) (4%) Is the total system...
2. Consider the system shown in the figure below, comprised of the same motor, steel beam,...
2. Consider the system shown in the figure below, comprised of the same motor, steel beam, steel cable and crate All assumptions and properties are the same with one exception; the cable is no longer considered as rigid Cable properties: length = 4 m, diameter = 0.007 m, E = 207 GPa, Calculate the equivalent stiffness of the cable, in units of N/m. (See table 4.1.1 in your textbook) Draw an equivalent system diagram where the beam and cable each...
Problem 111.3. A spin 1/2 particle interacts with a nnagnetic field B = Boe through the Pauli interaction H-μσ. B where μ is the magnetic moment. The Pauli spin matrices are İ-(Oz,@yMwwhere the σί are T0 1 0-il The eigenstates for d, are the spinors 0 (a) (3 pts.) Suppose that at time t-0 the particle is in an eigenstate Xx corresponding to spin pointing along the positive z-axis. Find the eigenstatexz in terms of α and β. (b) (7...
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...
1. Consider a quantum system comprising three indistinguishable particles which can occupy only three individual-particle energy levels, with energies ε,-0, ε,-2e and ε,-3. The system is in thermal equilibrium at temperature T. Suppose the particles are bosons with integer spin. i) How many states do you expect this system to have? Justify your answer [2 marks] (ii) Make a table showing, for each state of this system, the energy of the state, the number of particles (M, M,, N) with...
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...
3.3 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...
Match the following correctly principal quantum number, n=12.3 Al=0, 1, 2, 3, 4 B. designates size and energy C. s and p electrons outside noble gas or angular momentum quantum number, l-0 to (n-1) pseudo-noble gas core, involved in chemical reactions , p, d, f, g-which numbers? magnetic quantum number, m,--l to+1 spin quantum number m s=+1/2 or-1/2 Pauli Exclusion principle Aufbau Principle Hund's Rule pseudo-noble gas core D, no 2 electrons in an atom have the same 4 quantum...
Try to avoid handwriting please, thank you.
1. Consider the gas of electrons in gold, as in problem 3 above. (a) Begin by assuming the gas obeys classical statistics. Using the Som- merfeld model for the density of states, an analysis shows that the partition function in the MB distribution is given by (where V is the volume) m3/2v Plug this into the MB distribution and plot N(E) as a function of E. Assume a temperature T 300 K and...
Match the following correctly principal quantum number, n=12.3 Al=0, 1, 2, 3, 4 B. designates size and energy C. s and p electrons outside noble gas or angular momentum quantum number, l-0 to (n-1) pseudo-noble gas core, involved in chemical reactions , p, d, f, g-which numbers? magnetic quantum number, m,--l to+1 spin quantum number m s=+1/2 or-1/2 Pauli Exclusion principle Aufbau Principle Hund's Rule pseudo-noble gas core D, no 2 electrons in an atom have the same 4 quantum...
signals and systems
Question 1 (30%): Consider a LTI systern which is comprised of four subsystems whose impulse responses are hi(t), h2(t). ha(t), and ha(t). u(t) f(t) hi(t) h2(t) 13 ha(1) Where: hi (t) = δ(t + 1) h2(t) = 2(u(t)-u(t-1)] hs(t) = 201t-2) h1(t) = u(t + 2)-u(t) a) (8%) Compute the overall impulse response htotal(t) of the system comprised of hi(t), h2(t), hs(t), and h4(t). Sketch and write the expression for htotai(t) b) (4%) Is the total system...
2. Consider the system shown in the figure below, comprised of the same motor, steel beam, steel cable and crate All assumptions and properties are the same with one exception; the cable is no longer considered as rigid Cable properties: length = 4 m, diameter = 0.007 m, E = 207 GPa, Calculate the equivalent stiffness of the cable, in units of N/m. (See table 4.1.1 in your textbook) Draw an equivalent system diagram where the beam and cable each...
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