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 7.4, Problem 7.29P
To determine
The matrix elements of
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Problem 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?
Add the 2x2 identity matrix along with the three 2x2 Pauli matrices (see image 1), and show that any 2x2 matrix M can be written in the form (see image 2).
Note that the alpha "i" terms are complex numbers.
Suppose that you have the Lagrangian L = 21 (;² + è°r2) +
420
for a 2D
20
system in plane polar coordinates (r, 0).
Determine the pr and pe canonical coordinates.
Chapter 7 Solutions
Introduction To Quantum Mechanics
Ch. 7.1 - Prob. 7.1PCh. 7.1 - Prob. 7.2PCh. 7.1 - Prob. 7.3PCh. 7.1 - Prob. 7.4PCh. 7.1 - Prob. 7.5PCh. 7.1 - Prob. 7.6PCh. 7.2 - Prob. 7.8PCh. 7.2 - Prob. 7.9PCh. 7.2 - Prob. 7.10PCh. 7.2 - Prob. 7.11P
Ch. 7.2 - Prob. 7.12PCh. 7.2 - Prob. 7.13PCh. 7.3 - Prob. 7.15PCh. 7.3 - Prob. 7.16PCh. 7.3 - Prob. 7.17PCh. 7.3 - Prob. 7.18PCh. 7.3 - Prob. 7.19PCh. 7.3 - Prob. 7.20PCh. 7.3 - Prob. 7.21PCh. 7.3 - Prob. 7.22PCh. 7.4 - Prob. 7.23PCh. 7.4 - Prob. 7.24PCh. 7.4 - Prob. 7.25PCh. 7.4 - Prob. 7.26PCh. 7.4 - Prob. 7.27PCh. 7.4 - Prob. 7.28PCh. 7.4 - Prob. 7.29PCh. 7.5 - Prob. 7.31PCh. 7.5 - Prob. 7.32PCh. 7 - Prob. 7.33PCh. 7 - Prob. 7.34PCh. 7 - Prob. 7.35PCh. 7 - Prob. 7.36PCh. 7 - Prob. 7.37PCh. 7 - Prob. 7.38PCh. 7 - Prob. 7.39PCh. 7 - Prob. 7.40PCh. 7 - Prob. 7.42PCh. 7 - Prob. 7.43PCh. 7 - Prob. 7.44PCh. 7 - Prob. 7.45PCh. 7 - Prob. 7.46PCh. 7 - Prob. 7.47PCh. 7 - Prob. 7.49PCh. 7 - Prob. 7.50PCh. 7 - Prob. 7.51PCh. 7 - Prob. 7.52PCh. 7 - Prob. 7.54PCh. 7 - Prob. 7.56PCh. 7 - Prob. 7.57P
Knowledge Booster
Similar questions
- Check 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_forwardBit confused you say with is the definition of a complex conjugate but all I've ever seen is |X|^2=(X*)(X). Can you provide maybe a reference or proof of this?arrow_forwardi li. 9 V:OV docs.google.com/forms/d/e Which function is preferable to find the magnitude of a complex number? * sqrt() cart2pol() MATLAB does not support complex arguments abs() All matrices are vectors but all vectors are not matrices in MATLAB * False True Compute 24 modulo 5. b = mod(24,5) * b =6 b =4 b =5 b = 3 O Oarrow_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_forwardEvaluate the commutator è = [x², Pe** =?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_forward
- In terms of the totally antisymmetric E-symbol (Levi-Civita tensor) with €123 = +1, the vector product can be written as (A x B) i = tijk Aj Bk, where i, j, k = 1, 2, 3 and summation over repeated indices (here j and k) is implied. i) ii) iii) iv) For general vectors A and B, using (2) prove the following relations: a) A x B=-B x A b) (A x B) A = (A x B) - B = 0. The Levi-Civita symbol is related to the Kronecker delta. Prove the following very useful formula €ijk€ilm = 8j18km - Sjm³ki. (2) Prove the formula (3) €imn€jmn = 2dij. Assuming that (3) is true (and using antisymmetry of the E-symbol), prove the relation A x (B x C) = (AC) B- (AB) Carrow_forwardProve the following:arrow_forwardConsider the problem: [cput = (Koux)x+au, 0arrow_forwardProblem 2 Verify the Jacobi identity for Poisson brackets, {A, {B,C}} + {B, {C, A}} + {C, {A, B}} = 0 where the Poisson bracket is defined by n {X, Y} == Σ ΟΧ ΟΥ ΟΧ ΟΥ Әді дрі api əqi i=1 Here are the (canonical) coordinates, p; are the corresponding momenta, and n is the number of degrees of freedom.arrow_forwardEvaluate the spin matrices Sy and Szfor a particle with spin s = 1/2arrow_forwardConsider the three functions F (x₁, x2) = eª¹ + x₂; G (x₁, x₂) = x₂eª¹ + x₁e¹² and H = F (x₁, x2) — F(x2, x₁) x1 1 and 2 are particle labels. Which of the following statements are true? Both F and G are symmetric under interchange of particles G is symmetric under interchange of particles but not F OH is anti antisymmetric OF is neither symmetric nor antisymmetricarrow_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