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 5.3, Problem 5.27P
To determine
Show that most of the energies determined by Equation 5.71 are doubly degenerate and determine the exceptional cases.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
4.1 Calculate the three lowest energy levels, together with their degeneracies, for the
following systems (assume equal mass distinguishable particles).
a. Three noninteracting spin particles in a cubic box of side length L.
b. Four noninteracting spin particles in a cubic box of side length L.
PROBLEM 2 Calculate the probability distribution of momenta p for a ld
oscillator in the ground state (n = 0). Calculate the mean square dispersions
(x2), (p²), and the product (r2)(p²).
Draw an energy level diagram for a nonrelativistic particle confined inside a three-dimensional cube-shaped box, showing all states with energies below 15· (h2/8mL2). Be sure to show each linearly independent state separately, to indicate the degeneracy of each energy level. Does the average number of states per unit energy increase or decrease as E increases?
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
- Problem 1: Estimate the probability that a hydrogen atom at room temperature is in one of its first excited states (relative to the probability of being in the ground state). Don't forget to take degeneracy into account. Then repeat the calculation for a hydrogen atom in the atmosphere of the star y UMa, whose surface temperature is approximately 9500K.arrow_forwardProve that gn = g? + g + 2 for all n 21 is able to satisfy the recurrence relation equation gn = gn-1 + 2n. (That should say g sub(n-1) but my computer bugged up the format a little). Please show all steps.arrow_forwardA particle with a size just below r* is unstable but a particle with a size 2) just above r* is stable. What comments would you make on this statement? If you agree then, why are the particles just above (very little bigger than r*) a critical size r* thermodynamically stable even though the energy (Gibbs free energy) is positive. a) A 4G, surface energy 4xr'y AG Volume free energy Excess free energy AG. b) Why the free energy vs particle radius curves for homogeneous and heterogeneous nucleation differs. CAG, AG AG JAGeter AGomaarrow_forward
- PROBLEM 2. Consider a spherical potential well of radius R and depth Uo, so that the potential is U(r) = -Uo at r R. Calculate the minimum value of Uc for which the well can trap a particle with l = 0. This means that SE at Uo > Uc has at least one bound ground state at l = 0 and E < 0. At Ug = Uc the bound state disappears.arrow_forwardProblem # 2. In the two-level system, estimate the emission line full width at half maximum (FWHM) for spontaneous emission at 650 nm if the spontaneous radiative lifetime of the upper state is about 3,000 nanoseconds.arrow_forward(A) Consider a particle in a cubic box. What is the degeneracy of the level it hasenergy three times greater than that of the lowest level? (Explain the combinations of n that led you to the answer given). (B) The addition of sodium to ammonia generates a solvated electron that is trapped in a cavity of 0.3 nm in diameter, formed by ammonia molecules. The solvated electron can be modeled as a particle that moves freely inside the cubic box with ammonia molecules in the cube surface. If the length of the box is 0.3 nm, what energy is needed for the electron undergo a transition from a lower energy state to the subsequent state?arrow_forward
- Consider a system of 3 particles trapped in a box where there are 3 energy levels (non-degenerate and evenly spaced). The particles could be fermions, bosons, or simply distinguishable particles...for each of these three scenarios: What is the occupancy of the first excited state for each scenario?arrow_forwardThe ground state of the realistic Helium atom is nondegenerate. Let us now consider a hypothetical Helium atom where the two electrons are replaced by identical particles of spin 1 and negative charge. What is the degeneracy of the ground state? Explain your reasoning (ignore forces that depend on spin).arrow_forwardConsider a system of 3 particles trapped in a box where there are 3 energy levels (non-degenerate and evenly spaced). The particles could be fermions, bosons, or simply distinguishable particles... for each of these three scenarios: How many possible system states are there for this system? What is the occupancy of the first excited state for each scenario? If the temperature increases 3-fold, which state how has the highest occupancy? Discuss your observations on the previous questions in relation to whether the particles are bosons, fermions, or unknown distinguishable particles. a. b. C. d.arrow_forward
- Consider a system of 3 particles trapped in a box where there are 3 energy levels (non-degenerate and evenly spaced). The particles could be fermions, bosons, or simply distinguishable particles... for each of these three scenarios: What is the occupancy of the first excited state for each scenario?arrow_forward1) Consider a system consisting of two particles, each of which can occupy any one of three single-particle states, with energy 0, e and 2e. a) How many states are there if the particles are bosons? Write down the partition function for this system? b) function for this system? How many states are there if the particles are fermions? Write down the partitionarrow_forwardConsider two spin 1 particles, that can be combined to form j = 0, 1, 2 states. Use a method of your choosing to express the nine global eigenkets |j, m) in terms of the local eigenkets |j1, j1; m1, m2).arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
College PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage Learning
University Physics (14th Edition)PhysicsISBN:9780133969290Author:Hugh D. Young, Roger A. FreedmanPublisher:PEARSONIntroduction To Quantum MechanicsPhysicsISBN:9781107189638Author:Griffiths, David J., Schroeter, Darrell F.Publisher:Cambridge University Press
Physics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Lecture- Tutorials for Introductory AstronomyPhysicsISBN:9780321820464Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina BrissendenPublisher:Addison-Wesley
College Physics: A Strategic Approach (4th Editio...PhysicsISBN:9780134609034Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart FieldPublisher:PEARSON
College Physics
Physics
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Cengage Learning
University Physics (14th Edition)
Physics
ISBN:9780133969290
Author:Hugh D. Young, Roger A. Freedman
Publisher:PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:9781107189638
Author:Griffiths, David J., Schroeter, Darrell F.
Publisher:Cambridge University Press
Physics for Scientists and Engineers
Physics
ISBN:9781337553278
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:9780321820464
Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:Addison-Wesley
College Physics: A Strategic Approach (4th Editio...
Physics
ISBN:9780134609034
Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:PEARSON