Modern Physics For Scientists And Engineers
2nd Edition
ISBN: 9781938787751
Author: Taylor, John R. (john Robert), Zafiratos, Chris D., Dubson, Michael Andrew
Publisher: University Science Books,
expand_more
expand_more
format_list_bulleted
Question
error_outline
This textbook solution is under construction.
Students have asked these similar questions
How would I be able to sketch the graph in problem 7.36?
6.2.4 In the presence of a headwind of nor-
malized intensity W, your speed on your
bike is V = g(W) =
2010W ¹/3 mi/hr.
The wind intensity W is the continuous uni-
form (-1,1) random variable. (Note: If W
is negative, then the headwind is actually a
tailwind.) Find the PDF fv(v).
2.1 Consider a linear chain in which alternate ions have masses M₁ and M2, and only nearest
neighbors interact.
(1)
a/2
a
M₂
K
M₁
Show that the dispersion relation for normal modes is:
w ² (K) = K (1/₂ + 1/₂) + K
2
1
1
(₁+₂)
C
M₂
K
W
4
M₁M₂
-sin
(ka)
2
Where, K is the spring constant, and a, is the size of the unit cell (so the spacing
between atoms is a/2).
P
(ii) Derive an expression for the group velocity vg as a function of k.
(iii)
Use the results of part (ii), to evaluate vg for k at the Brillouin Zone boundary,[k = ±¹],
and briefly discuss the physical significance of this Brillouin Zone boundary group
velocity.(Specifically, what do you say about propagation of longitudinal waves in this
lattice at frequency w(k = ±"/a)?
(iv) Suppose that we allow the two masses M₁ and M2 in a one-dimensional diatomic lattice
to become equal. What happens with the frequency gap? Draw the dispersion relation
curve to support your answer (show your calculations).
Knowledge Booster
Similar questions
- QM 7.1 Answer question throughly and with much detail as possible. Include theory/ formulas if needed.arrow_forwardProblem 1.6.5. A magnetic moment µ in a magnetic field h has energy E+ = Fµh when it is parallel (antiparallel) to the field. Its lowest energy state is when it is aligned with h. probabilities for being parallel or antiparallel given by P(par)/P(antipar) = exp(-E+/T]/ exp[-E-/T] where T is the absolute temperature. Using the fact that the total probability must add up to 1, evaluate the absolute probabilities for the two orientations. Using this show that the average magnetic moment along the field h is m = µ tanh(uh/T) Sketch this as a function of temperature at fixed h. Notice that if h = 0, m vanishes since the moment points up and down with %3D However at any finite temperature, it has a nonzero %3D equal probability. Thus h is the cause of a nonzero m. Calculate the susceptibility, dm lh=0 as a function of T.arrow_forwardProblem 1.17 A particle is represented (at time=0) by the wave function A(a²-x²). if-a ≤ x ≤+a. 0, otherwise. 4(x, 0) = { (a) Determine the normalization constant A. (b) What is the expectation value of x (at time t = 0)? (c) What is the expectation value of p (at time t = 0)? (Note that you cannot get it from p = md(x)/dt. Why not?) (d) Find the expectation value of x². (e) Find the expectation value of p².arrow_forward
- Legrende polynomials The amplitude of a stray wave is defined by: SO) =x (21+ 1) exp li8,] sen 8, P(cos 8). INO Here e is the scattering angle, / is the angular momentum and 6, is the phase shift produced by the central potential that performs the scattering. The total cross section is: Show that: 'É4+ 1)sen² 8, .arrow_forwardIn Problems 3 to 12, find the average value of the function on the given interval. Use equation (4.8) if it applies. If an average value is zero, you may be able to decide this from a quick sketch which shows you that the areas above and below the x axis are the same. 11. sin a + sin x on (0, 27)arrow_forward• 5.1. A two-mirror resonator is formed by a convex mirror of radius R, -1 m and a concave mirror of radius R, = 1.5 m. What is the maximum possible mirror separation if this is to remain a stable resonator? 5.17. An unstable resonator consists of a plane mirror (mirror 1) and a convex mirror (mirror 2) of radius of curvature R, = 2 m, spaced by a distance L = 50 cm. Calculate: The resonator location in the g,, 2. plane.arrow_forward
- 1.2 From the figure below (i) Determine the Miller indices for the plane. (ii) Let the length of all the three base vectors of the direct lattice a = 5 nm. Calculate the distance of the lattice planes (346).arrow_forwardShow that a gaussian psi (x) = e ^(-ax^2) can be an eigenfunction of H(hat) for harmonic oscillator 1. Compute T(hat)*psi 2. Compute Vhat* psi - assume V operator is 1/2w^2x^2 3. Write out Hbar*psi and identify terms so Hber*psi=E*psi is true 4. From cancellation find a 5. insert back a to Schrodinger eq above and find Earrow_forward2.2. (a) Verify explicitly the invariance of the volume element do of the phase space of a single particle under transformation from the Cartesian coordinates (x,y, z, px, Py, Pz) to the spherical polar coordinates (r,e,4,Pr.Pe,Po). (b) The foregoing result seems to contradict the intuitive notion of "equal weights for equal solid angles," because the factor sine is invisible in the expression for do. Show that if we average out any physical quantity, whose dependence on po and po comes only through the kinetic energy of the particle, then as a result of integration over these variables we do indeed recover the factor sin0 to appear with the subelement (de do).arrow_forward
- QM 6.1. Answer question throughly and with much detail as possible. Include formulas/ all work.arrow_forwardSection 1.3 Space Lattices 1.1 Determine the number of atoms per unit cell in a (a) face-centered cubic, (b) body-centered cubic, and (c) diamond lattice.arrow_forwardBased from the sample prob. 2.10. Then answer PRACTICE EXERCISE 2.10 with Complete solutionsarrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- College PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage LearningUniversity 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 LearningLecture- Tutorials for Introductory AstronomyPhysicsISBN:9780321820464Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina BrissendenPublisher:Addison-WesleyCollege 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