Use the Levi Civit a symbol to prove that (a) (A B) (C D) (A C)(B D) (A D)(B C) (b) (f g) g ( f) f ( g) (c) (A B) (C D) (A C D)B (B C D)A (d) The 2 2 Pauli matrices x , y , and z used in quantum mechanics satisfy i j ij i ijk k If a and b are ordinary vectors, prove that ( a)( b) a b i (a b) ...

Use the Levi-Civit`a symbol to prove that (a) (A B) (C D) = (A

Question:

Use the Levi-Civit`a symbol to prove that
(a) (A × B) · (C × D) = (A · C)(B · D) − (A · D)(B · C).

(b) ∇ · (f × g) = g · (∇ ×f) − f · (∇ ×g).

(d) The 2 × 2 Pauli matrices σ_x, σ_y , and σ_z used in quantum mechanics satisfy σ_iσ_j = δ_ij + iε_ijk^σk . If a and b are ordinary vectors, prove that (σ · a)(σ · b) = a · b + iσ · (a × b).

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Modern Electrodynamics

ISBN: 9780521896979

1st Edition

Authors: Andrew Zangwill

See More Books

Question Posted: Feb 02, 2023 01:17 AM

See More Questions

Use mathematical induction to prove that a b is a factor of an bn whenever n is a positive integer.
determine x y And z components of moment of force about point O The force F = {300 i 100 j- 700 k} lb acts at the end of the beam (Figure 1). Figure 1.5 ft B 0.25 ft F 8 ft < 1 of 1 Copyright 2022 Pe
Prove that v = x + i y and v- = x - i y are linearly independent complex vectors if and only if their real and imaginary parts x and y are linearly independent real vectors.
We are given a number of darts. Suppose it is known that each time we throw a dart at a target, we have a probability of 1/4 of hitting the target. An experiment consists of throwing three darts at...
Refer to the previous exercise. The data file contains price, weight, and type of suspension system (FU = full, FE = front-end in the scatterplot shown). a. Do you observe a linear relationship? Is...
How far apart must two point charges of 75.0 nC (typical of static electricity) be to have a force of 1.00 N between them?
Suppose that linear regression is used to estimate factorial effects for a $2^{k}$ design by doubling the estimated regression coefficients. a. When is it possible to estimate the standard error of...
Assume that the tax rate is 35 percent. You can borrow at 8 percent before taxes. Should you lease or buy? You work for a nuclear research laboratory that is contemplating leasing a diagnostic...
Murphee Manufacturing is considering purchasing a machine with an expected life of 8 years for $68,000. The machine has an estimated salvage value of $4,000, Murphee expects the new machine to...
Ben Swanson, owner and manager of Swansons Department Store, has decided to use statistical forecasting to get a better handle on the demand for his major products. However, Ben now needs to decide...
Use the Levi-Civita symbol to prove that. (a) (f g) = f g + g f. (b) (f g) = f g gf. (c) (g r) = 2g + r g/r r( g).
Evaluate the following expressions which exploit the Einstein summation convention. (a). ii. (b). ij ijk. (c). ijk jk. (d). ijk ijk.
Mrs. Beard recognized a $12,290 loss on the sale of corporate stock this year. How much loss can she deduct in each of the following cases? a. She had no other capital transactions this year. b. She...
Given the information below answer the questions. Depreciation Expense-Building 12,000 12,000 Repairs Expense 8,850 8,850 feedba Depreciation Expense-Equipment 4,800 4,800 Insurance Expense 3,150...
5. (5 pts) Explain what is wrong with the following method definition. public static void SubtractNumbers (int x, int y) { return x + y; }
Presented below is financial information for two different companies. Determine the missing amounts. Sales revenue Sales discounts Sales returns Vaughn Company Tamarisk Company $194,000 3,400 3,900...
What is the output of the following code? int a = 3; int b = 5; int c = 8; if (a > 0 && b < c 1 c > 8) { System.out.println("true"); } else { } System.out.println("false");
what is the output of the following code? int main() { } int a=5; int *p=&a; ++a; cout < < a**p; Answer:
Let z0 = x0, z1 = x0, z2 = x1, and z3 = x1. Form the following divided-difference table. Show that the cubic Hermite polynomial H3(x) can also be written as f [z0] + f [z0, z1](x x0) + f [z0, z1,...
With your classmates, form small teams of skunkworks. Your task is to identify an innovation that you think would benefit your school, college, or university, and to outline an action plan for...
Write the chemical reactions (including structures of reactants and products) that occur when the amino acid histidine is titrated with perchloric acid. (Histidine is a molecule with no net charge.)...
Select indicators from Table 10-3 that would be useful for the titrations in Figures 10-1 and 10-2 and the pK a = 8 curve in Figure 10-3. Select a different indicator for each titration and state...
Select indicators from Table 10-3 that would be useful for the titrations in Figures 10-1 and 10-2 and the pK a = 8 curve in Figure 10-3. Select a different indicator for each titration and state...
Financial data for Joel de Paris, Incorporated, for last year follow: Joel de Paris, Incorporated Balance Sheet Assets Cash Accounts receivable Inventory Plant and equipment, net Beginning Balance...
The Alpine House, Incorporated, is a large retailer of snow skis. The company assembled the information shown below for the quarter ended March 31: Sales Selling price per pair of skis Variable...
The fastener division of Marigold Fasteners manufactures zippers and then sells them to customers for $7.40 per unit. Its variable cost is $3.24 per unit, and its fixed cost per unit is $1.72....

Use the Levi-Civit`a symbol to prove that (a) (A B) (C D) = (A

Question:

Step by Step Answer:

a b c d A x B C x D Eijk A...View the full answer

Modern Electrodynamics

Students also viewed these Engineering questions