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 4.4, Problem 4.41P
To determine
The commutator of
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
Describe all vectors in span{(3,0,2), (-2,0,3)} (so computationally what do the vectors look like?). Also give a geometric description for these vectors (what space are you in and visually what do you get? Be as descriptive as you can!).
Consider 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)
I have an 2x2 matrix such that
a
(5)
, where a,b,c,d lies in the x-y plane. I need to apply
rotation matrices to rotate this matrix in the
following manner.
1. The rotation is along the x axis by angle theta
2. The rotation is along the y axis by angle theta
3. The rotation is along the z axis by angle theta
NOTE! Clearly state the theory to derive the
rotation matrices for all the cases. State the rotation
matrices and show with an example that it works
for all cases.
Chapter 4 Solutions
Introduction To Quantum Mechanics
Ch. 4.1 - Prob. 4.1PCh. 4.1 - Prob. 4.3PCh. 4.1 - Prob. 4.4PCh. 4.1 - Prob. 4.5PCh. 4.1 - Prob. 4.6PCh. 4.1 - Prob. 4.7PCh. 4.1 - Prob. 4.8PCh. 4.1 - Prob. 4.9PCh. 4.1 - Prob. 4.10PCh. 4.1 - Prob. 4.11P
Ch. 4.2 - Prob. 4.12PCh. 4.2 - Prob. 4.13PCh. 4.2 - Prob. 4.14PCh. 4.2 - Prob. 4.15PCh. 4.2 - Prob. 4.16PCh. 4.2 - Prob. 4.17PCh. 4.2 - Prob. 4.18PCh. 4.2 - Prob. 4.19PCh. 4.2 - Prob. 4.20PCh. 4.3 - Prob. 4.21PCh. 4.3 - Prob. 4.22PCh. 4.3 - Prob. 4.23PCh. 4.3 - Prob. 4.24PCh. 4.3 - Prob. 4.25PCh. 4.3 - Prob. 4.26PCh. 4.3 - Prob. 4.27PCh. 4.4 - Prob. 4.28PCh. 4.4 - Prob. 4.29PCh. 4.4 - Prob. 4.30PCh. 4.4 - Prob. 4.31PCh. 4.4 - Prob. 4.32PCh. 4.4 - Prob. 4.33PCh. 4.4 - Prob. 4.34PCh. 4.4 - Prob. 4.35PCh. 4.4 - Prob. 4.36PCh. 4.4 - Prob. 4.37PCh. 4.4 - Prob. 4.38PCh. 4.4 - Prob. 4.39PCh. 4.4 - Prob. 4.40PCh. 4.4 - Prob. 4.41PCh. 4.5 - Prob. 4.42PCh. 4.5 - Prob. 4.43PCh. 4.5 - Prob. 4.44PCh. 4.5 - Prob. 4.45PCh. 4 - Prob. 4.46PCh. 4 - Prob. 4.47PCh. 4 - Prob. 4.48PCh. 4 - Prob. 4.49PCh. 4 - Prob. 4.50PCh. 4 - Prob. 4.51PCh. 4 - Prob. 4.52PCh. 4 - Prob. 4.53PCh. 4 - Prob. 4.54PCh. 4 - Prob. 4.55PCh. 4 - Prob. 4.56PCh. 4 - Prob. 4.57PCh. 4 - Prob. 4.58PCh. 4 - Prob. 4.59PCh. 4 - Prob. 4.61PCh. 4 - Prob. 4.62PCh. 4 - Prob. 4.63PCh. 4 - Prob. 4.64PCh. 4 - Prob. 4.65PCh. 4 - Prob. 4.66PCh. 4 - Prob. 4.70PCh. 4 - Prob. 4.72PCh. 4 - Prob. 4.73PCh. 4 - Prob. 4.75PCh. 4 - Prob. 4.76P
Knowledge Booster
Similar questions
- Calculate the commutators [^px2, f(^x)].arrow_forwardProve the Jacobi identity: A × (B × C) + B × (C × A) + C × (A × B) = 0. Hint:Expand each triple product as in equations (3.8) and (3.9).arrow_forwardFind the line integral of F(x, y, z) = x°i + y°j+ zk along the line segment C from the origin to the point (4, 2, 6). F. dr =arrow_forward
- Consider the following scalar and vectors: A = 41+ 3) + 7k T = 3x+8yz + 2zx 1. Calculate for the Laplacian of vector the function 2. Calculate the divergence of Aarrow_forwardEvaluate the commutator è = [x², Pe** =?arrow_forwardCheck if the following operators with the corresponding functions could form an eigen value equations or not (where Bis a constant value) No. function Оperator 3 2 3 sin(ßx) sin(Bx) d dx 4 sin(ßx) dxarrow_forward
- d² Let  = Consider the orthonormal basis: dx² |1) = ₁(x) = [2) = ₂(x) = √sin(x) L 2π sin and (a) Find Â1) and Â12). The operator  can be expressed in a matrix form as follows:  = a₁1)(1| + a₁21)(2 + a21 2)(1| + a2212X<21. (b) Use part (a) to compute: amn= (m|Â\n); m, n = 1,2.arrow_forwardProblem 3: Two-level system and density matrice Suppose a 2 x 2 matrix X (not necessarily Hermitian or unitary) is written as X = a000 + a.σ, where ao and ak, k = 1, 2, 3, are numbers, 0o = 1 is the identity matrix and o are the Pauli matrices. (a) How are ao and a related to tr(X) and tr(OX)? Obtain ao and ak in terms of the matrix elements Xij. Assume that ao, ak ER such that X is Hermitian and could be interpreted as a Hamiltonian, what are the eigenvalues of X?arrow_forwardFor each of the following vector fields F , decide whether it is conservative or not by computing the appropriate first order partial derivatives. Type in a potential function f (that is, Vf = F) with f(0,0) = 0. If it is not conservative, type N. A. F (x, y) = (4x – 2y) i+ (-2x + 12y) j f (x, y) = B. F (x, y) = 2yi+ 3xj f (x, y) = C. F (x, y) = (2 sin y) i + (–4y + 2x cos y) j f (x, y) = Note: Your answers should be either expressions of x and y (e.g. "3xy + 2y"), or the letter "N"arrow_forward
- Two particles, each of mass m, are connected by a light inflexible string of length l. The string passes through a small smooth hole in the centre of a smooth horizontal table, so that one particle is below the table and the other can move on the surface of the table. Take the origin of the (plane) polar coordinates to be the hole, and describe the height of the lower particle by the coordinate z, measured downwards from the table surface. i. sketch all forces acting on each mass ii. explain how we get the following equation for the total energyarrow_forwardFind the Laplacian of each of the following scalar functions. a) V= x^2 + 2xy + 3z +4 b) Φ = sin[x] x sin[y] x sin[z] c) W = (e^-5x)(sin[4y]) x cos[3z]arrow_forwardConsider the following unattached spring system. m₁ = 1, C₁ = 14, Ea{ } m₂ = 7 Write the stiffness matrix K = Write the matrix M-¹K Find the eigenvalues and eigenvectors of M-¹K: • Smaller eigenvalue = with eigenvector • Larger eigenvalue = with eigenvector If the spring system oscillates beginning with initial displacement u(0) = [8] and initial velocity u'(0) = u₁(t) = u₂(t) = Find a nonzero initial velocity vector such that the displacement of the masses will be bounded. • u'(0) = | -22 then compute the displacements of the masses at time t. 10arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_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