Introduction To Quantum Mechanics
3rd Edition
ISBN: 9781107189638
Author: Griffiths, David J., Schroeter, Darrell F.
Publisher: Cambridge University Press
expand_more
expand_more
format_list_bulleted
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
Want to see more full solutions like this?
Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
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
Knowledge Booster
Similar questions
- (2nx sin \1.50. 2nz Consider the case of a 3-dimensional particle-in-a-box. Given: 4 = sin(ny) sin 2.00. What is the energy of the system? O 6h?/8m O 4h²/8m O 3h2/8m O none are correctarrow_forwardHarmonic oscillator eigenstates have the general form 1 μω ,1/4 μω AG)(√(-) n ħ In this formula, which part determines the number of nodes in the harmonic oscillator state? = y (x) 1 √(™ ћn 2"n! Holev 1/4 μω 1 2"n! exp(-1022²) 2ħ μω ħ 2"n! exp μω χ 2ħ 2arrow_forwardIn a gas identical, weakly interacting particles in a state with degeneracy 6 has 4 particles. The number of ways selecting the particles in the state under FD, MB, and BE distributions respectively 30, 256, 256 (b) 15, 1296, 126 (c) 30, 256, 63 (d) 15, 1296, 216arrow_forward
- Consider a system of N non - interacting particles. Each particle is fixed in position and can sit in two possible states which, for convenience, we will cal "spin up" |t) and "spin down" |↓). We take the energy of these states to be E=0, E_1 = \epsi the system has N_↑ particles with spin up and N_↓ = N - N_t particles with spin down. Find the final state of the system if E_< < E_↑arrow_forwardThe energy eigenvalues of a particle in a 3-D box of dimensions (a, b, c) is given by E (nx, ny, nz) -2²² (²²² +²2² +²2²) (a) Ten protons are confined in a box of dimension (a, 2a, a) on each side. Calculate the total energy of the ground state of these ten protons if we assume that the protons don't interact with each other. (b) If the ten protons are replaced by 10 neutral hydrogen atoms in the ground state, calculate the total energy resulting from the confinement. Again assume that the hydrogen atoms do not interact with each other. You can treat the mass of proton and hydrogen atom to be identical.arrow_forwardA particle is confined in a box of length L as shown in the figure. If the potential is treated as a perturbation, including the first order correction, the ground state energy is (a) E = ħ²π² 2mL² + V (b) E = ħ²π² Vo 2mL² ħ²π² Vo ħ²π² Vo (c) E = + (d) E = + 2mL² 4 2mL² L/2arrow_forward
- Consider an atom with two states having ground state energy zero and first excited state energy 1 eV. Determine the partition function for the atom at 3000 K. (a) 1.0407 (b) 1.0547 (c) 1.0822 (d) 1.0209arrow_forward(a) Derive an expression for the variance in the number of particles in a state for a Bose- Einstein gas when the number of particles in the gas can change. (b) Using the particle number for the Bose-Einstein gas, determine any specific properties of the chemical potential.arrow_forwardConsider a 10000 distinguishable particles at room temperature, 298 K. Suppose that each particle has 2 energy levels, 0.01 eV and 0.02 eV. Find the number of the particles in each energy level. ( Boltzmann's constant is 1.3807 × 10-23 J K-1.)arrow_forward
- A particle of massm in a harmonic oscillator potential with angular frequency w is in the state (1 + {t)쭈 What is (p?) for this particle? mhw 2 O 6mħw O 3mhwarrow_forwardext cenb. Consider a system whose states are given in term of complete and orthonormal set of kets |1>, |2 >, [3 >,14 > as follows: 1 1p >= |1 > + 기2 > +2|3 > + 기4 > i 214> Where the kets |n > are eigenstates of an observable A defined on the system as follows: 2 A]n > = na|n > with n = 1,2,3,4 and with a a constant number. have 4) eiyen vealue 1. If A is measured, which values will be found and with which probabilities? 2. Find the expectation value of A for the state |Ø >. 3. Assume that the state 14> is found after the measurement of A. If A is measured again immediately, which states will be found and with which probabilities? 4. Find the expectation value of A if the system is in the state |4 >. 5. Assume B another observable defined on the system, which is compatible with A. Write the uncertainty inequality between A and B. 6. If B is measured, which states will be found and with which probabilities?arrow_forwardProblem 3: Chemical potential of an Einstein solid. Consider an Einstein solid for which both N and q are much greater than 1. Think of each ocillator as a separate “particle". a) Show that the chemical potential is H = -kT In (**e) b) Discuss this result in the limits N » q and N « q, concentrating on the question of how much S increases when another particle carrying no energy is added to the system. Does the formula make intuitive sense?arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Classical Dynamics of Particles and SystemsPhysicsISBN:9780534408961Author:Stephen T. Thornton, Jerry B. MarionPublisher:Cengage Learning
Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning
Modern PhysicsPhysicsISBN:9781111794378Author:Raymond A. Serway, Clement J. Moses, Curt A. MoyerPublisher:Cengage Learning
Classical Dynamics of Particles and Systems
Physics
ISBN:9780534408961
Author:Stephen T. Thornton, Jerry B. Marion
Publisher:Cengage Learning
Principles of Physics: A Calculus-Based Text
Physics
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Physics for Scientists and Engineers: Foundations...
Physics
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Cengage Learning
Modern Physics
Physics
ISBN:9781111794378
Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher:Cengage Learning