![Fundamentals of Physics, Volume 1, Chapter 1-20](https://www.bartleby.com/isbn_cover_images/9781118233764/9781118233764_largeCoverImage.gif)
Fundamentals of Physics, Volume 1, Chapter 1-20
10th Edition
ISBN: 9781118233764
Author: David Halliday
Publisher: WILEY
expand_more
expand_more
format_list_bulleted
Question
Chapter 38, Problem 64P
To determine
To show:
The angular wave number for a nonrelativistic free particle of mass m can be written as
where,
Expert Solution & Answer
![Check Mark](/static/check-mark.png)
Want to see the full answer?
Check out a sample textbook solution![Blurred answer](/static/blurred-answer.jpg)
Students have asked these similar questions
Solid metals can be modeled as a set of uncoupled harmonic oscillators of the same
frequency with energy levels given by
En = ħwn
n = 0, 1, 2,...
where the zero-point energy (the lowest energy state) of each oscillator has been adjusted
to zero for simplicity. In this model, the harmonic oscillators represent the motions of the
metal atoms relative to one another. The frequency of these oscillators is low so that
ħw
= = 224
KB
and the system vibrational partition function is given by
3N
Z
² = la₁ -
(1
1
e-0/T).
(a) If the system contains one mole of atoms, find the average energy (in J) of this system at
T= 172 K. (You can use =
BkB.)
T
(b) What is the absolute entropy (in J/K) for this system? You can use either the Gibbs
expression for S, or the system partition function to make this evaluation (they are
equivalent, as your reading assignment indicates).
Harmonic 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
2
(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 correct
Chapter 38 Solutions
Fundamentals of Physics, Volume 1, Chapter 1-20
Ch. 38 - Prob. 1QCh. 38 - Prob. 2QCh. 38 - Prob. 3QCh. 38 - Prob. 4QCh. 38 - Prob. 5QCh. 38 - Prob. 6QCh. 38 - Prob. 7QCh. 38 - Prob. 8QCh. 38 - Prob. 9QCh. 38 - Prob. 10Q
Ch. 38 - Prob. 11QCh. 38 - Prob. 12QCh. 38 - Prob. 13QCh. 38 - Prob. 14QCh. 38 - Prob. 15QCh. 38 - Prob. 16QCh. 38 - Prob. 1PCh. 38 - Prob. 2PCh. 38 - Prob. 3PCh. 38 - Prob. 4PCh. 38 - Prob. 5PCh. 38 - Prob. 6PCh. 38 - Prob. 7PCh. 38 - Prob. 8PCh. 38 - Prob. 9PCh. 38 - Prob. 10PCh. 38 - Prob. 11PCh. 38 - Prob. 12PCh. 38 - Prob. 13PCh. 38 - Prob. 14PCh. 38 - Prob. 15PCh. 38 - Prob. 16PCh. 38 - Prob. 17PCh. 38 - Prob. 18PCh. 38 - Prob. 19PCh. 38 - Prob. 20PCh. 38 - Prob. 21PCh. 38 - Prob. 22PCh. 38 - Prob. 23PCh. 38 - Prob. 24PCh. 38 - Prob. 25PCh. 38 - Prob. 26PCh. 38 - Prob. 27PCh. 38 - Prob. 28PCh. 38 - Prob. 29PCh. 38 - Prob. 30PCh. 38 - Prob. 31PCh. 38 - Prob. 32PCh. 38 - Prob. 33PCh. 38 - Prob. 34PCh. 38 - Prob. 35PCh. 38 - Prob. 36PCh. 38 - Prob. 37PCh. 38 - Prob. 38PCh. 38 - Prob. 39PCh. 38 - Prob. 40PCh. 38 - Prob. 41PCh. 38 - Prob. 42PCh. 38 - Prob. 43PCh. 38 - Prob. 44PCh. 38 - Prob. 45PCh. 38 - Prob. 46PCh. 38 - Prob. 47PCh. 38 - Prob. 48PCh. 38 - Prob. 49PCh. 38 - Prob. 50PCh. 38 - Prob. 51PCh. 38 - Prob. 52PCh. 38 - Prob. 53PCh. 38 - Prob. 54PCh. 38 - Prob. 55PCh. 38 - Prob. 56PCh. 38 - Prob. 57PCh. 38 - Prob. 58PCh. 38 - Prob. 59PCh. 38 - Prob. 60PCh. 38 - Prob. 61PCh. 38 - Prob. 62PCh. 38 - Prob. 63PCh. 38 - Prob. 64PCh. 38 - Prob. 65PCh. 38 - Prob. 66PCh. 38 - Prob. 67PCh. 38 - Prob. 68PCh. 38 - Prob. 69PCh. 38 - Prob. 70PCh. 38 - Prob. 71PCh. 38 - Prob. 72PCh. 38 - Prob. 73PCh. 38 - Prob. 74PCh. 38 - Prob. 75PCh. 38 - Prob. 76PCh. 38 - Prob. 77PCh. 38 - Prob. 78PCh. 38 - Prob. 79PCh. 38 - Prob. 80PCh. 38 - Prob. 81PCh. 38 - Prob. 82PCh. 38 - Prob. 83PCh. 38 - Prob. 84PCh. 38 - Prob. 85PCh. 38 - Prob. 86PCh. 38 - Prob. 87PCh. 38 - Prob. 88PCh. 38 - Prob. 89PCh. 38 - Prob. 90P
Knowledge Booster
Similar questions
- If the ground state energy of a simple harmonic oscillator is 1.25 eV, what is the frequency of its motion?arrow_forwardAn H2 molecule can be approximated by a simple harmonic oscillator with a force constant k = 1.1 x 103 N/m. Find (a) the energy levels and (b) the possible wavelengths of photons emitted when the H2 molecule decays from the third excited state eventually to the ground state.arrow_forwardA system of three identical distinguishable particles has energy 3ɛ. The single particle can take discrete energies 0, &, 2, 3ɛ and so on. The average number of particles in the energy state & is 1.2 0.9 0.6 0.3arrow_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_forwardA particle of mass m is subjected to a force F(r) = -VV(r) such that the wave function p(p, t) satisfies the momentum-space Schrödinger equation %3D (p²/2m – aV,) p(p, t) = idp(p, t)/ôt, %3D where h = 1, a is some real constant and V; = /dp? + 8² /əp", + a² /ðp? . Find the force F (r).arrow_forwardYou have the energy matrix for only 4x4 elements. Calculate the expected value of energy (E) using the function 1 1 -fox /2 e -3icut 2 [e heo S 0 0 0 2 E= = 5 0 0 e 0 2 0 0 0 Ther 2 J Al Laxities (E) A8l 2 gidd) dasll Cuaal l o |2 l Jiew /2 Vi *[fi“ e 0:‘ 5arrow_forward
- At time t = 0, a free particle is in a state described by the normalised wave function V(x, 0) where = L A(k) eikz dk, 2π 1/2 a A(k) = (-¹² e-d³²k²/2, and where a is a real positive constant. Estimate the probability that, at time t = 0, the particle's momentum is in the range 1.99h/a ≤ hk ≤ 2.01h/a.arrow_forwardFind the angular momentum and kinetic energy in the z axis for the (cos(30))*e(iΦ)+(sin(30))*e(-iΦ) wave function.arrow_forwardA particle with mass m is in the state тс V (x,t) = Ae +iat 2h where A and a are positive real constants. Calculate the potential energy function that satisfies the Schrodinger equation.arrow_forward
- A particle with mass m is moving in three-dimensions under the potential energy U(r), where r is the radial distance from the origin. The state of the particle is given by the time-independent wavefunction, Y(r) = Ce-kr. Because it is in three dimensions, it is the solution of the following time-independent Schrodinger equation dıp r2 + U(r)µ(r). dr h2 d EÞ(r) = 2mr2 dr In addition, 00 1 = | 4ar?y? (r)dr, (A(r)) = | 4r²p²(r)A(r)dr. a. Using the fact that the particle has to be somewhere in space, determine C. Express your answer in terms of k. b. Remembering that E is a constant, and the fact that p(r) must satisfy the time-independent wave equation, what is the energy E of the particle and the potential energy U(r). (As usual, E and U(r) will be determined up to a constant.) Express your answer in terms of m, k, and ħ.arrow_forwardU = U, %3D U = 0 X = 0 A potential step U(x) is defined by U(x) = 0 for x 0 If an electron beam of energy E > U, is approaching from the left, write the form of the wave function in region I (x 0) in terms of the electron mass m, energy E, and potential energy U,. Do not bother to determine the constant coefficients. Formulas.pdf (Click here-->) Edit Vicw Insert Format Tools Table 12pt v Paragraph BIU Av eu T? varrow_forward+8 x a nd described by the wave function y(x)= Bsin(kx). Determine i) The energy levels, the omentum, the wave length, the parity and number of nodes for the states n = 1, 2 3 and 4. Suppose V=10 J in the box. What effect has this on a) eigenvalues? b) the eigen functions?arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningPrinciples of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningUniversity Physics Volume 3PhysicsISBN:9781938168185Author:William Moebs, Jeff SannyPublisher:OpenStax
![Text book image](https://www.bartleby.com/isbn_cover_images/9781133939146/9781133939146_smallCoverImage.gif)
Physics for Scientists and Engineers: Foundations...
Physics
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Cengage Learning
![Text book image](https://www.bartleby.com/isbn_cover_images/9781133104261/9781133104261_smallCoverImage.gif)
Principles of Physics: A Calculus-Based Text
Physics
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
![Text book image](https://www.bartleby.com/isbn_cover_images/9781938168185/9781938168185_smallCoverImage.gif)
University Physics Volume 3
Physics
ISBN:9781938168185
Author:William Moebs, Jeff Sanny
Publisher:OpenStax