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 3.6, Problem 3.23P
To determine
To show that the projection operators are idempotent, and to determine the Eigen values of
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Find the following commutators by applying the operators to an arbitrary function f(x)
[e, x + d²/dx²]
[x³ — d/dx, x+d²/dx²]
Consider the matrix representation of Lx, Ly and L₂ for the case l = 1 (see Matrix Representation of
Operators class notes pp. 11-12).
(a) Construct the matrix representation of L² for l = 1.
(b) What are the eigenvalues and corresponding eigenvectors of L²?
(c) Are the eigenvectors of L² the same as those of L₂? Explain.
(d) Compute L² |x; +1), where |x;+1) is the eigenvector of La corresponding to eigenvalue +ħ.
For the spherical polar coordinates (r,theta,phi) prove that their unit vectors are mutially orthogonal?
Chapter 3 Solutions
Introduction To Quantum Mechanics
Ch. 3.1 - Prob. 3.1PCh. 3.1 - Prob. 3.2PCh. 3.2 - Prob. 3.3PCh. 3.2 - Prob. 3.4PCh. 3.2 - Prob. 3.5PCh. 3.2 - Prob. 3.6PCh. 3.3 - Prob. 3.7PCh. 3.3 - Prob. 3.8PCh. 3.3 - Prob. 3.9PCh. 3.3 - Prob. 3.10P
Ch. 3.4 - Prob. 3.11PCh. 3.4 - Prob. 3.12PCh. 3.4 - Prob. 3.13PCh. 3.5 - Prob. 3.14PCh. 3.5 - Prob. 3.15PCh. 3.5 - Prob. 3.16PCh. 3.5 - Prob. 3.17PCh. 3.5 - Prob. 3.18PCh. 3.5 - Prob. 3.19PCh. 3.5 - Prob. 3.20PCh. 3.5 - Prob. 3.21PCh. 3.5 - Prob. 3.22PCh. 3.6 - Prob. 3.23PCh. 3.6 - Prob. 3.24PCh. 3.6 - Prob. 3.25PCh. 3.6 - Prob. 3.26PCh. 3.6 - Prob. 3.27PCh. 3.6 - Prob. 3.28PCh. 3.6 - Prob. 3.29PCh. 3.6 - Prob. 3.30PCh. 3 - Prob. 3.31PCh. 3 - Prob. 3.32PCh. 3 - Prob. 3.33PCh. 3 - Prob. 3.34PCh. 3 - Prob. 3.35PCh. 3 - Prob. 3.36PCh. 3 - Prob. 3.37PCh. 3 - Prob. 3.38PCh. 3 - Prob. 3.39PCh. 3 - Prob. 3.40PCh. 3 - Prob. 3.41PCh. 3 - Prob. 3.42PCh. 3 - Prob. 3.43PCh. 3 - Prob. 3.44PCh. 3 - Prob. 3.45PCh. 3 - Prob. 3.47PCh. 3 - Prob. 3.48P
Knowledge Booster
Similar questions
- Suppose that A,, is a covector field, and consider the object Fμv=O₁ Av - O₂ A₁. (a) Show explicitly that F is a tensor, that is, show that it transforms appropriately under a coordinate transformation.arrow_forwardConsider the following operator imp Â= and the following functions that are both eigenfunctions of this operator. mm (0) = e² ‚ (ø) = (a) Show that a linear combination of these functions d² dø² is also an eigenfunction of the operator. (b) What is the eigenvalue? -m imp c₁e¹m + c₂e² -imp -imp = earrow_forwardCalculate the commutators [^px2, f(^x)].arrow_forward
- Suppose that A is a covector field, and consider the object Fμ = 0μA, O₂ A₁. (a) Show explicitly that F is a tensor, that is, show that it transforms appropriately under a coordinate transformation. (b) Show that the definition F = V₁A₂-V₂A, which uses the covariant derivative, is equiv- alent to the definition above.arrow_forwardThe transformation relating Cartesian and cylindrical coordinate is p = (x² + y²)2 0 = tan-12 x = p cos 0, y = p sin 0 , z = z, Show that the gradient operator in cylindrical coordinates is given by z = z 1. V= pa, +÷ôaq + 2əzarrow_forwardCompute and sketch the vector assigned to the points P = (0, 6, –1) and Q = (4, 1,0) by the vector field F = (xy, z? , x). F(P) = F(Q) =arrow_forward
- Consider the vector field F ,32 Is this vector field Conservative? Select an answer v If so: Find a function f so that F = V f f(x,y) = + K Use your answer to evaluate F. dī along the curve C: T(t) = 2 cos(t)i + 2 sin(t)j, 0arrow_forward(a) Let F₁ = x² 2 and F₂ = x x + y ŷ + z 2. Calculate the divergence and curl of F₁ and F₂. Which one can be written as the gradient of a scalar? Find a scalar potential that does the job. Which one can be written as the curl of a vector? Find a suitable vector potential. (b) Show that the field F3 = yz î + zx ŷ + xy 2 can be written both as the gradient of a scalar and as the curl of a vector. Find scalar and vector potentials for this function.arrow_forwardFor each of the following vector fields F , decide whether it is conservative or not by computing curl F . Type in a potential function f (that is, ∇f=F). F(x,y)=(−3siny)i+(10y−3xcosy)jarrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
Recommended textbooks for you
Classical Dynamics of Particles and SystemsPhysicsISBN:9780534408961Author:Stephen T. Thornton, Jerry B. MarionPublisher:Cengage Learning
Classical Dynamics of Particles and Systems
Physics
ISBN:9780534408961
Author:Stephen T. Thornton, Jerry B. Marion
Publisher:Cengage Learning