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Part B
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Question 3 (MCQ...
5. The following statements related to classical particles, bosons and fermions are true a. Their spin...
5. The following statements related to classical particles, bosons and fermions are true a. Their spin states do not matter for the distinction. b. fermions have half integer spin. c. All are indistinguishable. d. None are indistinguishable. e. Only classical particles can, in principle, be distinguished from each other. f. Classical particles are always spin 1. 6. The pressures of gases at the same temperature and density made of classical particles, fermions or bosons have these characteristics a. The pressure...
[1 44= 9 marks ] Question 5 Consider two identical particles in 1D which exist in single-particle (normalised) (x), and...
[1 44= 9 marks ] Question 5 Consider two identical particles in 1D which exist in single-particle (normalised) (x), and are in such close proximity they can be considered as indistinguishable. wave functions /a(x) and (a) Write down the symmetrised two-particle wave function for the case where the particles are bosons (VB) and the case where the particles are fermions (Vp). (b) Show that the expectation value (xjr2)B,F is given by: (T122) в,F — (а:)a (х)ь + dx x y:(")...
trying for last time :( Can anyone please help and explain how to do this task...
trying for last time :( Can anyone please help and explain how
to do this task ? Thank you
Q4 (QUANTUM IDEAL GASES) Is the statement "Given a two-spinless-fermion system, and two orbitals o labeled by quantum numbers a, b, the two-body wavefunction (1,2 represent the particle variables) V (1, 2) = 0a(1)$a (2) - 06(1)$6(2) +0a(1)º(2) - 06(1)$a(2) correctly describes a possible state of the system” true or false ? Explain your answer (0.5p). 4b) Consider a Fermi gas...
Question 3 a) Consider the hypothetical case of two degenerate quantum levels of energy E1, E2...
Question 3 a) Consider the hypothetical case of two degenerate quantum levels of energy E1, E2 (E. < Ez) and statistical weights g1 = 4, 92 = 2. These levels have respective populations N1 = 3 and N2 = 1 particles. What are the possible microstates if the particles are (1) bosons (6 marks) or (ii) fermions (6 marks)? AP3, PHA3, PBM3 PS302 Semester One 2011 Repeat page 2 of 5 b) Show how the number of microstates would be...
referencing: 3-6. Use either the expression for (E) in Example 3-1 or the one in Problem...
referencing:
3-6. Use either the expression for (E) in Example 3-1 or the one in Problem 3-5 to show that hy B and that (E)-→ 0 T→00 as Postulate That the Average Ensemble Energy Is Equal to the Observed Energy of a System ls EXAMPLE 3-1 uation for (E) for the simple system of a (bare) proton in a magnetic eld B ON: The energy of a bare proton in a magnetic field B, is given by Ey y is...
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...
Question 5 [2 + 2 + 2 + 3 + 3 = 12 marks ] (a)...
Question 5 [2 + 2 + 2 + 3 + 3 = 12 marks ] (a) Briefly explain why we cannot find simultaneous eigenfunctions of Lg, Ly and Lz. An electron in a hydrogen atom is in the n = 2 state. Ignoring spin, write down the list of possible quantum numbers {n, l, m}. (b) For two qubits briefly explain, giving examples, the difference between a product state and an entangled state (c) Consider a system of identical bosons...
[ 2 + 2 + 2 + 3 + 3 = 12 marks ] Question 5 (a) Briefly explain why we cannot find simultaneous eigenfunctions of Lt, L...
[ 2 + 2 + 2 + 3 + 3 = 12 marks ] Question 5 (a) Briefly explain why we cannot find simultaneous eigenfunctions of Lt, L, and Lz. An electron in a hydrogen atom is in the n = 2 state. Ignoring spin, write down the list of possible quantum numbers {n, l, m} (b) For two qubits briefly explain, giving examples, the difference between a product state and an entangled state (c) Consider a system of identical...
Question 9 Consider a quantum system comprising two indistinguishable particles which can occupy only three individual-particle...
Question 9 Consider a quantum system comprising two indistinguishable particles which can occupy only three individual-particle energy levels, with energies 81 0, 82 2 and E3 38.The system is in thermal equilibrium at temperature T. (a) Suppose the particles which can occupy an energy level. are spinless, and there is no limit to the number of particles (i) How many states do you expect this system to have? Justify your answer (ii) Make a table showing, for each state of...
KURSVLOEBEUR Question 4 [20 marks] (a) What particular aspect of the Rayleigh-Jeans Law, the classical theory...
KURSVLOEBEUR Question 4 [20 marks] (a) What particular aspect of the Rayleigh-Jeans Law, the classical theory of blackbody radiation, caused it to fail to explain the blackbody radiation spectrum? (b) What aspect of the Boltzmann probability distribution used in formulating Planck's Law of blackbody radiation allows it to avoid the problem that caused the classical model to "crash and burn" i.e. not match experiment? (c) In a low energy electron diffraction (LEED) experiment, 62 eV electrons are scattered from the...
5. The following statements related to classical particles, bosons and fermions are true a. Their spin states do not matter for the distinction. b. fermions have half integer spin. c. All are indistinguishable. d. None are indistinguishable. e. Only classical particles can, in principle, be distinguished from each other. f. Classical particles are always spin 1. 6. The pressures of gases at the same temperature and density made of classical particles, fermions or bosons have these characteristics a. The pressure...
[1 44= 9 marks ] Question 5 Consider two identical particles in 1D which exist in single-particle (normalised) (x), and are in such close proximity they can be considered as indistinguishable. wave functions /a(x) and (a) Write down the symmetrised two-particle wave function for the case where the particles are bosons (VB) and the case where the particles are fermions (Vp). (b) Show that the expectation value (xjr2)B,F is given by: (T122) в,F — (а:)a (х)ь + dx x y:(")...
trying for last time :( Can anyone please help and explain how
to do this task ? Thank you
Q4 (QUANTUM IDEAL GASES) Is the statement "Given a two-spinless-fermion system, and two orbitals o labeled by quantum numbers a, b, the two-body wavefunction (1,2 represent the particle variables) V (1, 2) = 0a(1)$a (2) - 06(1)$6(2) +0a(1)º(2) - 06(1)$a(2) correctly describes a possible state of the system” true or false ? Explain your answer (0.5p). 4b) Consider a Fermi gas...
Question 3 a) Consider the hypothetical case of two degenerate quantum levels of energy E1, E2 (E. < Ez) and statistical weights g1 = 4, 92 = 2. These levels have respective populations N1 = 3 and N2 = 1 particles. What are the possible microstates if the particles are (1) bosons (6 marks) or (ii) fermions (6 marks)? AP3, PHA3, PBM3 PS302 Semester One 2011 Repeat page 2 of 5 b) Show how the number of microstates would be...
referencing:
3-6. Use either the expression for (E) in Example 3-1 or the one in Problem 3-5 to show that hy B and that (E)-→ 0 T→00 as Postulate That the Average Ensemble Energy Is Equal to the Observed Energy of a System ls EXAMPLE 3-1 uation for (E) for the simple system of a (bare) proton in a magnetic eld B ON: The energy of a bare proton in a magnetic field B, is given by Ey y is...
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...
Question 5 [2 + 2 + 2 + 3 + 3 = 12 marks ] (a) Briefly explain why we cannot find simultaneous eigenfunctions of Lg, Ly and Lz. An electron in a hydrogen atom is in the n = 2 state. Ignoring spin, write down the list of possible quantum numbers {n, l, m}. (b) For two qubits briefly explain, giving examples, the difference between a product state and an entangled state (c) Consider a system of identical bosons...
[ 2 + 2 + 2 + 3 + 3 = 12 marks ] Question 5 (a) Briefly explain why we cannot find simultaneous eigenfunctions of Lt, L, and Lz. An electron in a hydrogen atom is in the n = 2 state. Ignoring spin, write down the list of possible quantum numbers {n, l, m} (b) For two qubits briefly explain, giving examples, the difference between a product state and an entangled state (c) Consider a system of identical...
Question 9 Consider a quantum system comprising two indistinguishable particles which can occupy only three individual-particle energy levels, with energies 81 0, 82 2 and E3 38.The system is in thermal equilibrium at temperature T. (a) Suppose the particles which can occupy an energy level. are spinless, and there is no limit to the number of particles (i) How many states do you expect this system to have? Justify your answer (ii) Make a table showing, for each state of...
KURSVLOEBEUR Question 4 [20 marks] (a) What particular aspect of the Rayleigh-Jeans Law, the classical theory of blackbody radiation, caused it to fail to explain the blackbody radiation spectrum? (b) What aspect of the Boltzmann probability distribution used in formulating Planck's Law of blackbody radiation allows it to avoid the problem that caused the classical model to "crash and burn" i.e. not match experiment? (c) In a low energy electron diffraction (LEED) experiment, 62 eV electrons are scattered from the...
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