Modern Physics
2nd Edition
ISBN: 9780805303087
Author: Randy Harris
Publisher: Addison Wesley
expand_more
expand_more
format_list_bulleted
Question
Chapter 7, Problem 42E
To determine
To Rewrite:The given equation as
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
In spherical polar coordinates, the angular momentum operators, 1² and Îz, can be written,
Ә
β = -ħ²
1 ə
sin Ꮎ ᎧᎾ
1 2²
sin² 0 00²
дф
él
sin)+ +
and
(a) îψ(θ, φ) = λιψ(θ, φ)
=
Î₂ = = -ih
Apply these operators to the unnormalized eigenfunction, (0, 4) = sin²0 e-²ip, and
determine the eigenvalues of that are associated with each operator.
(b) Î₂¥(0, 0) = 1₂4(0,4)
QUESTION 3: Abstract angular momentum operators: In this problem you may assume t
commutation relations between the general angular momentum operators Ĵ, Ĵy, Ĵz. Use whenev
possible the orthonormality of normalised angular momentum eigenstate |j, m) and that
α = Îx±iĴy, Ĵ²|j,m) = ħ²j(j + 1)|j,m) and Ĵz|j,m)
(a) Express ĴĴ_ in terms of Ĵ² and Ĵ₂.
=
ħmlj, m).
(b) Using the result from (a) find the expectation value (j,m|εÎ_|j,m). (This is the nor
squared of the state Î_|j,m).)
Consider the Laplace's equation u t uyy = 0 in the square 00 find the associated eigenfunctions X,(x) forn= 1,2,3, -
c) Using the boundary condition calculate Y, y)
d) Calculate the coefficients (c,) to satisfy the nonhomogeneous condition
e) Write a formal series solution of the problem.
Chapter 7 Solutions
Modern Physics
Ch. 7 - Prob. 1CQCh. 7 - Prob. 2CQCh. 7 - Prob. 3CQCh. 7 - Prob. 4CQCh. 7 - Prob. 5CQCh. 7 - Prob. 6CQCh. 7 - Prob. 7CQCh. 7 - Prob. 8CQCh. 7 - Prob. 9CQCh. 7 - What are the dimensions of the spherical harmonics...
Ch. 7 - Prob. 11CQCh. 7 - Prob. 12CQCh. 7 - Prob. 13CQCh. 7 - Prob. 14CQCh. 7 - Prob. 15CQCh. 7 - Prob. 16CQCh. 7 - Prob. 17ECh. 7 - Prob. 18ECh. 7 - Prob. 19ECh. 7 - Prob. 20ECh. 7 - Prob. 21ECh. 7 - Prob. 22ECh. 7 - Prob. 23ECh. 7 - Prob. 24ECh. 7 - Prob. 25ECh. 7 - Prob. 26ECh. 7 - Prob. 27ECh. 7 - Show that of hydrogen’s spectral seriesLyman,...Ch. 7 - Prob. 29ECh. 7 - Prob. 30ECh. 7 - Prob. 31ECh. 7 - Prob. 32ECh. 7 - Prob. 33ECh. 7 - Prob. 34ECh. 7 - Prob. 35ECh. 7 - Prob. 36ECh. 7 - Prob. 37ECh. 7 - A particle orbiting due to an attractive central...Ch. 7 - Prob. 39ECh. 7 - Prob. 40ECh. 7 - Prob. 41ECh. 7 - Prob. 42ECh. 7 - Prob. 43ECh. 7 - How many different 3d states are there? What...Ch. 7 - Prob. 45ECh. 7 - Prob. 46ECh. 7 - Prob. 47ECh. 7 - Prob. 48ECh. 7 - Prob. 49ECh. 7 - Prob. 50ECh. 7 - Prob. 51ECh. 7 - Prob. 52ECh. 7 - Prob. 53ECh. 7 - Prob. 54ECh. 7 - For states where l=n1 , the radial probability...Ch. 7 - Prob. 56ECh. 7 - Prob. 57ECh. 7 - Prob. 58ECh. 7 - Prob. 59ECh. 7 - Prob. 60ECh. 7 - Prob. 61ECh. 7 - Prob. 62ECh. 7 - Prob. 63ECh. 7 - Prob. 64ECh. 7 - Prob. 65ECh. 7 - Prob. 66ECh. 7 - Prob. 67ECh. 7 - Prob. 68ECh. 7 - Prob. 69ECh. 7 - Prob. 70ECh. 7 - Prob. 71ECh. 7 - Prob. 72ECh. 7 - Prob. 73ECh. 7 - Prob. 74ECh. 7 - Prob. 75ECh. 7 - Prob. 76ECh. 7 - Prob. 77ECh. 7 - Prob. 78ECh. 7 - Prob. 79CECh. 7 - Prob. 80CECh. 7 - Prob. 81CECh. 7 - Prob. 83CECh. 7 - Prob. 84CECh. 7 - Prob. 85CECh. 7 - Prob. 86CECh. 7 - Prob. 87CECh. 7 - Prob. 89CE
Knowledge Booster
Similar questions
- Evaluate the commutator è = [x², Pe** =?arrow_forwardConsider a rectangular surface of length L and width W in the xy plane with its center at the origin: Which of the following are valid expressions for the area vector of this surface? Check all that apply. O (0,0, LW) O (W, L, 0) O (0,0, -LW) O (LW, LW, 0) O (0, LW, 0) O (L, W, 0)arrow_forwardConvert points P(1,3,5), T(0, -4, 3), and S(-3,-4,-10) from Cartesian to cylindrical and spherical coordinates.arrow_forward
- The surface integral of V = x + yŷ + (z - 3)2 over the sphere of unit radius centred at the origin is Select one: ○ a. 4π ○ b. O ○ c. 4π/3 ○ d. πarrow_forwardIs the function Ψ = xe−x^2/2 an eigenfunction of the operator Aˆ = −∂2/∂x2+ x2 ?arrow_forwardConsider the function v(1,2) =( [1s(1) 3s(2) + 3s(1) 1s(2)] [x(1) B(2) + B(1) a(2)] Which of the following statements is incorrect concerning p(1,2) ? a. W(1,2) is normalized. Ob. The function W(1,2) is symmetric with respect to the exchange of the space and the spin coordinates of the two electrons. OC. y(1,2) is an eigenfunction of the reference (or zero-order) Hamiltonian (in which the electron-electron repulsion term is ignored) of Li with eigenvalue = -5 hartree. d. The function y(1,2) is an acceptable wave function to describe the properties of one of the excited states of Lit. Oe. The function 4(1,2) is an eigenfunction of the operator S,(1,2) = S;(1) + S,(2) with eigenvalue zero.arrow_forward
- Given the potential function V = x2y(z+3), determine the electric potential at (3, 4, -6).arrow_forwardA triangle in the xy plane is defined with corners at (x, y) = (0,0), (0, 2) and (4, 2). We want to integrate some function f(x, y) over the interior of this triangle. Choosing dx as the inner integral, the required expression to integrate is given by: Select one: o Sro S-o f(x, y) dx dy x=0 2y y=0 O S-o So F(x, y) dæ dy O o S f(x, y) dy dæ O So So F(x, y) dx dy x/2 =0arrow_forwardConsider a composite state of an electron with total angular momentum j1 = 1/2 and a proton with angular momentum j2 = 3/2. Find all the eigenstates of |j1,j2;j,m⟩ as the linear combination of product states of angular momentum of electron and proton |j1,j2;m1,m2⟩. Give the values of Clebsch-Gordon coefficients you get from here. If the system is found in state |j1 = 1/2,j2 = 3/2;j = 1,m = −1⟩, what is the probability that j1z = −1/2 and what is the probability that j1z = 1/2arrow_forward
- Find an equation for the plane through the points (-6, 8, – 1) and (-1,3, –8) and perpendicular to the plane -4x – 3y + 8z = 10. An equation for the plane is ...arrow_forwardLet V = 2xyz3 +3 In(x² + 2y² + 3z²) V in free space. Evaluate each of the following quantities at P(3, 2, –1): (a) V; (b) |V|; (c) E; (d) |E|; (e) a (f) D.arrow_forwardThe angular momentum operator is given by Î = î × p. (a) Assuming we are in cartesian space, prove that [Li, Lj]— = iħ€¡jk (b) Define the ladder operators as L₁ = L₁ iL2. Show that L² = L + L= F ħL3 + L². kLk.arrow_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