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(29.2) For the particles considered in Example 29.2, what is the probability that both particles are...
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...
2. Two noninteracting particles, each of mass m, are in the 1-D harmonic oscillator potential Describe...
2. Two noninteracting particles, each of mass m, are in the 1-D harmonic oscillator potential Describe their ground state and the next two excited states, that is, their corresponding (i) wave functions, (i) energy eigenvalues, and (ii) degeneracies if two particles are (a) distinguishable particles, (b) the identical bosons, and (c) the identical fermions. 3. Suppose one particle is in the ground state, and the other is in the first excited state for tw particles described in Prob. 2. Calculate...
1. Imagine that a particle can exist in one of the three states: |0 > , |1 >, |2> . We now consider 2 such part...
1. Imagine that a particle can exist in one of the three states: |0 > , |1 >, |2> . We now consider 2 such particles. How many distinguishable states are possible if the particles are (a) distinguishable (b) indistinguishable, classic (c) bosons (d) fermions. Write down the wave function of the system for all cases.
2096) Two noninteracting particles 1 and 2, each of mass m, are in a 1-D infinite...
2096) Two noninteracting particles 1 and 2, each of mass m, are in a 1-D infinite square well ol width a. If one is in the state V'in and the other in the state (n! /), calculate C(xI-x), assuming (a) (6%) they are distinguishable particles, (b) (7%) Ihey are identical bosons, and (c) (796) Ihey arc identical fermions. 4.
Q1: Consider two particles occupying the ground state 01) and the first excited state (42) of...
Q1: Consider two particles occupying the ground state 01) and the first excited state (42) of the one dimensional infinite square potential well. Give a proper form of the normalized wave function of the system (11,12) in the following cases: (a) The two particles are distinguishable. (b) The two particles are identical bosons. (c) The two particles are identical fermions
[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...
10.13. (a) Consider the helium atom to be a fixed point nucleus (charge 2e) with two...
10.13. (a) Consider the helium atom to be a fixed point nucleus (charge 2e) with two spin-half fermion elec trons. What is the degeneracy of its ground state? (That is, how many independent states of the whole atom have the ground state energy?) (b) Suppose instead that the electron was a spin-half boson. (It is an experimental fact that all spin-half particles are fermions, but there is nothing to stop us imagining a spin-half boson.) What then would be the...
Statistical_Mechanics 2 20 points) 2D ideal Fermi gas 24 Consider an ideal Fermi gas in 2D....
Statistical_Mechanics
2 20 points) 2D ideal Fermi gas 24 Consider an ideal Fermi gas in 2D. It is contained in an area of dimensions L x L. The particle mass is m. (a) Find the density of states D(e) N/L2 (b) Find the Fermi energy as a function of the particle density n = (c) Find the total energy as a function of the Fermi energy ef. (d) Find the chemical potential u as a function of n and T....
hat would be the partition function of this system according to equa tion 7.16? (e) W...
hat would be the partition function of this system according to equa tion 7.16? (e) W (f) What is the probability of finding both particles in the same single-par state, for the three cases of distinguishable particles, identical bosons, ane identical fermions? 4) The entropy of a two-state para magnet is given by S = Nk [ln(2 cosh x )-x tanhx ]], where x 2 uB kT Find the value of S at T-0 and T-oo. sinhx = "(ex-c"); coshx-(ex...
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...
2. Two noninteracting particles, each of mass m, are in the 1-D harmonic oscillator potential Describe their ground state and the next two excited states, that is, their corresponding (i) wave functions, (i) energy eigenvalues, and (ii) degeneracies if two particles are (a) distinguishable particles, (b) the identical bosons, and (c) the identical fermions. 3. Suppose one particle is in the ground state, and the other is in the first excited state for tw particles described in Prob. 2. Calculate...
2096) Two noninteracting particles 1 and 2, each of mass m, are in a 1-D infinite square well ol width a. If one is in the state V'in and the other in the state (n! /), calculate C(xI-x), assuming (a) (6%) they are distinguishable particles, (b) (7%) Ihey are identical bosons, and (c) (796) Ihey arc identical fermions. 4.
Q1: Consider two particles occupying the ground state 01) and the first excited state (42) of the one dimensional infinite square potential well. Give a proper form of the normalized wave function of the system (11,12) in the following cases: (a) The two particles are distinguishable. (b) The two particles are identical bosons. (c) The two particles are identical fermions
[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...
10.13. (a) Consider the helium atom to be a fixed point nucleus (charge 2e) with two spin-half fermion elec trons. What is the degeneracy of its ground state? (That is, how many independent states of the whole atom have the ground state energy?) (b) Suppose instead that the electron was a spin-half boson. (It is an experimental fact that all spin-half particles are fermions, but there is nothing to stop us imagining a spin-half boson.) What then would be the...
Statistical_Mechanics
2 20 points) 2D ideal Fermi gas 24 Consider an ideal Fermi gas in 2D. It is contained in an area of dimensions L x L. The particle mass is m. (a) Find the density of states D(e) N/L2 (b) Find the Fermi energy as a function of the particle density n = (c) Find the total energy as a function of the Fermi energy ef. (d) Find the chemical potential u as a function of n and T....
hat would be the partition function of this system according to equa tion 7.16? (e) W (f) What is the probability of finding both particles in the same single-par state, for the three cases of distinguishable particles, identical bosons, ane identical fermions? 4) The entropy of a two-state para magnet is given by S = Nk [ln(2 cosh x )-x tanhx ]], where x 2 uB kT Find the value of S at T-0 and T-oo. sinhx = "(ex-c"); coshx-(ex...
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