An Introduction to Thermal Physics
1st Edition
ISBN: 9780201380279
Author: Daniel V. Schroeder
Publisher: Addison Wesley
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 8.2, Problem 25P
In problem 8.15 you manually computed the energy of a particular state of a
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Problem 8.3 Show that the Bose-Hubbard model has the superfluid ground
state at integer µ/U for any value of hopping by using the degenerate pertur-
bation theory.
4. (Kittel 7.4) Chemical potential versus temperature. Explain graphically why the
initial curvature of u versus 7 is upward for a fermion gas in one dimension and
downward in three dimensions (Figure 7.7).
Hint: The D₁(e) and D, (e) curves are different, where D, is given in Problem 1. It
will be found useful to set up the integral for N, the number of particles, and to
consider from the graphs the behavior of the integrand between zero temperature and
a finite temperature.
Draw a typical dispersion relation curve (w-k curve ) for Vp=Vg and Vp not equal to Vg where Vp is the phase velocity and Vg the group velocity .
Also the image for the delta w and delta k values are attached in a photo below . There are 9 values .
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Similar questions
- I only need help with problem 4. The answer is E = 86 meV 1. For a potential barrier with V(x) = 0 for |x| > a/2, and V(x) = 0.3 eV for |x| < a/2, 4. Consider the potential barrier discussed in problem 1. Suppose that there are two of these barriers forming a double‐barrier structure. If they are separated by 5 nm, what are the resonant energy level(s) in the well?arrow_forwardProblem 1: Two-level system. Canonical ensemble. Consider N impurity atoms trapped in a solid matrix. Each impurity can be in one of two states, with energies 0 and ɛ, respectively. The energy level are non-degenerate. 1) Compute the partition function Z, for one subsystem (i.e. one impurity atom). 2) Compute the partition function Z for the system. 3) Deduce the free energy. 4) Deduce the entropy. 5) Deduce the internal energy. Problem 2: Two-level system. Canonical ensemble. Redo the above problem. We assume that the ground level is non degenerate and the excited level is g-fold degenerate.arrow_forwardFor Problem 8.16, how do I prove the relations and give the correct expressions?arrow_forward
- A half-infinite well has an infinitely high wall at the origin and one of finite height U_0 at x = L. The number of allowed states is limited just like the finite well. Making an assumption that it has only two energy states, E1 and E2, where E2 is not much below U_0.a. Make a sketch of the potential energy, then add plausible sketches of the two allowed wave functions on separate horizontal axes whose heights are E1 and E2.arrow_forwardHow do I prove that the transition is successful in problem 7.22?arrow_forwardFor a unit cell with the set of real crystal lattice vectors a1 = (9.96,0,0) a2 = (5.58, 12.7,0) az = (-1.31, -4.33,4.75) Calculate the dot product of the real and reciprocal lattice vectors: a1 b2 Report your result to 2 decimal places.arrow_forward
- Problem 3: Harmonic oscillator. Canonical ensemble. Consider a system of N harmonic oscillators. We assume that the oscillators are distinguishable, one-dimensional, practically independent and having the same angular frequency w. 1) Compute the partition function Z, for one subsystem (i.e. harmonic oscillator). 2) Compute the partition function Z for the system. 3) Deduce the free energy. 4) Deduce the entropy. 5) Deduce the internal energy.arrow_forward1.7 A crystal has a basis of one atom per lattice point and a set of primitive translation vectors (in A): c = 1.5(i + j+ k), a = 3i, where i, j and k are unit vectors in the x, y and z directions of a Cartesian coordinate system. What is the Bravais lattice type of this crystal, and what are the Miller indices of the set of planes most densely populated with atoms? Calculate the volumes of the primitive unit cell and the conventional unit cell. b= 3j.arrow_forwardHarmonic oscillator. Canonical ensemble. Consider a system of N harmonic oscillators. We assume that the oscillators are distinguishable, one-dimensional, practically independent and having the same angular frequency w. 1) Compute the partition function Z, for one subsystem (i.e. harmonic oscillator). 2) Compute the partition function Z for the system. 3) Deduce the free energy. 4) Deduce the entropy. 5) Deduce the internal energy.arrow_forward
- Q#1 Verify Divergence Theorem for F =xi + j + yzk, taken over the cube bounded by x= 0, x = 1, y = 0, y = 1, z = 0, z = 1.arrow_forwardProblem 4. Consider two indistinguishable, noninteracting spin-1/2 fermions in a one- dimensional infinite square well potential of length L. (a) What is the ground-state energy of the two-particle system? (b) What is the ground-state quantum state vector? (c) What is the first excited state energy of the two-particle system? (d) What are the quantum state vectors of the first excited state? (e) What is the degeneracy of the first excited state? (f) Discuss qualitatively how the excited-state energies change if we consider the particles to be interacting through the Coulomb potential.arrow_forwardPROBLEM 1. Calculate the normalized wave function and the energy level of the ground state (1 = 0) for a particle in the infinite spherical potential well of radius R for which U(r) = 0 at r R. HINT: Reduce the spherically-symmetric SE to a ld form using the substi- tution (r) = x(r)/r.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:PEARSON
Introduction 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
Ising model | A Bird's Eye View | Solid State Physics; Author: Pretty Much Physics;https://www.youtube.com/watch?v=1CCZkHPrhzk;License: Standard YouTube License, CC-BY