Introduction To Quantum Mechanics
3rd Edition
ISBN: 9781107189638
Author: Griffiths, David J., Schroeter, Darrell F.
Publisher: Cambridge University Press
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Question
Chapter 5, Problem 5.29P
(a)
To determine
The number of different three particle states can be constructed from three distinguishable particles.
(a)
Expert Solution
Answer to Problem 5.29P
The number of different three particle states can be constructed from three distinguishable particles are
Explanation of Solution
Each distinguishable particle can have
Therefore, the total number of states the three particle can have be
Conclusion:
Thus, the number of different three particle states can be constructed from three distinguishable particles are
(b)
To determine
The number of different three particle states can be constructed from three identical bosons.
(b)
Expert Solution
Answer to Problem 5.29P
The number of different three particle states can be constructed from three identical bosons are
Explanation of Solution
If all particles are in same state:
If two particles are in same state:
It all three particles are in different states:
Therefore, the total number of state the three particles states can be constructed from identical bosons are
Conclusion:
Thus, the number of different three particle states can be constructed from three identical bosons are
(c)
To determine
The number of different three particle states can be constructed from three identical fermions.
(c)
Expert Solution
Answer to Problem 5.29P
The number of different three particle states can be constructed from three identical fermions is
Explanation of Solution
Fermions must occupy different states.
All three particles are in different states:
Therefore, the total number of state the three particles states can be constructed from identical fermions is
Conclusion:
Thus, the number of different three particle states can be constructed from three identical fermions is
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Students have asked these similar questions
(a) Construct the completely antisymmetric wave function ψ(xA, xB, xC) for three identical fermions, one in the state ψ5, one in the state ψ7, and one in the state ψ17.
(b) Construct the completely symmetric wave function ψ(xA, xB, xC) for three identical bosons, (i) if all three are in state ψ11, (ii) if two are in state ψ1 and one is in state ψ19, and (iii) if one is in the state ψ5, one in the state ψ7, and one in the state ψ17.
For a system of 4 distinguishable particles to be distributed in 6 allowed energy states namely E0 (0 eV), E1 (1 eV), E2 (2 eV), E3 (3 eV), E4 (4 eV), and E5 (5 eV) (for convenience you can call energy states as compartments/boxes), find total number of microstates corresponding to the condition “E0 box” contains 2 particles and total energy remains 3 eV. Also draw the schematic diagram showing distinguishable particles occupying the energy levels.
A particle with mass m is in a field and has the state (in spherical coordinates) :
Where N > 0 and a > 0 are fixed numbers. Determine the average kinetic energy of the particles.
Chapter 5 Solutions
Introduction To Quantum Mechanics
Ch. 5.1 - Prob. 5.1PCh. 5.1 - Prob. 5.2PCh. 5.1 - Prob. 5.3PCh. 5.1 - Prob. 5.4PCh. 5.1 - Prob. 5.5PCh. 5.1 - Prob. 5.6PCh. 5.1 - Prob. 5.8PCh. 5.1 - Prob. 5.9PCh. 5.1 - Prob. 5.10PCh. 5.1 - Prob. 5.11P
Ch. 5.2 - Prob. 5.12PCh. 5.2 - Prob. 5.13PCh. 5.2 - Prob. 5.14PCh. 5.2 - Prob. 5.15PCh. 5.2 - Prob. 5.16PCh. 5.2 - Prob. 5.17PCh. 5.2 - Prob. 5.18PCh. 5.2 - Prob. 5.19PCh. 5.3 - Prob. 5.20PCh. 5.3 - Prob. 5.21PCh. 5.3 - Prob. 5.22PCh. 5.3 - Prob. 5.23PCh. 5.3 - Prob. 5.24PCh. 5.3 - Prob. 5.25PCh. 5.3 - Prob. 5.26PCh. 5.3 - Prob. 5.27PCh. 5 - Prob. 5.29PCh. 5 - Prob. 5.30PCh. 5 - Prob. 5.31PCh. 5 - Prob. 5.32PCh. 5 - Prob. 5.33PCh. 5 - Prob. 5.34PCh. 5 - Prob. 5.35PCh. 5 - Prob. 5.36PCh. 5 - Prob. 5.38PCh. 5 - Prob. 5.39P
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