Consider two operators (mathbf{A}) and B. Show that [e^{-i mathbf{A}} e^{-i mathbf{B}}=e^{-i(mathbf{A}+mathbf{B})}] only if (mathbf{A}) and (mathbf{B})

Question:

Consider two operators $\mathbf{A}$ and B. Show that

\[e^{-i \mathbf{A}} e^{-i \mathbf{B}}=e^{-i(\mathbf{A}+\mathbf{B})}\]

only if $\mathbf{A}$ and $\mathbf{B}$ commute.

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

Step by Step Answer:

Related Book For answer-question

An Introduction To Groups And Their Matrices For Science Students

ISBN: 9781108831086

1st Edition

Authors: Robert Kolenkow

See More Books

Question Posted: Mar 16, 2024 09:52 AM

See More Questions

s1 educated (SSE) student for every three public school educated (PSE) students. Reasoning that students are not very dissimilar from threads, he suggests the following entry and exit routines be...
Microkernel operating systems aim to address perceived modularity and reliability issues in traditional "monolithic" operating systems. (i) Describe the typical architecture of a microkernel...
Let r and s be solutions to the quadratic equation x 2 b x + c = 0. For n N, define d0 = 0 d1 = r s dn = b dn1 c dn2 (n 2) Prove that dn = r n s n for all n N. [4 marks] (b) Recall that a commutative...
Erin Danielle Company purchased equipment and incurred the following costs. What amount should be recorded as the cost of the equipment? (a) $24,000. (c) $25,400. (b) $25,200. (d) $25,800. Cash price...
How does the flow of current differ in a superconductor compared with the flow in ordinary conductors?
A steam power plant operating in an ideal Rankine cycle has a high pressure of 5 MPa and a low pressure of 15 kPa. The turbine exhaust state should have a quality of at least 95% and the turbine...
Abbott Industries is a well-known supplier of pharmaceuticals worldwide. Founded by Dr. Wallace Abbott, the company was incorporated in 1900 after he had been developing and making pharmaceuticals...
Ram Roys firm has developed the following supply, demand, cost, and inventory data. Allocate production capacity to meet demand at a minimum cost using the transportation method. What is the cost?...
(1) (a) Discretize the 2D Poisson equation Vu(x, y) = Uxx + Uyy = = p(x, y) with second-order accurate central differences with Ax = the given charge density. Ay=h. p(x, y) is (b) Express uij in...
Show that the angular momentum operators $\left(I_{x}, I_{y}, I_{z}ight)$ are Hermitian.
Diagonalize this Pauli spin matrix, \[\frac{\hbar}{2}\left(\begin{array}{cc}0 & -i \\i & 0\end{array}ight)\] and find its eigenvalues.
Cable TV revenue. Data for cable TV revenue are given in the table for the years 2003 through 2007. (A) Find the least squares line for the data, using x = 0 for 2000. (B) Use the least squares line...
A three phase transmission line has a resistance of 10 and reactance of 80 per wire. The load current is 90 A and the power factor of the load is 80% lagging. The sending (generator) end voltage in...
A boat in a lock with lock door A a water height of 4 . 2 m . Lock door B a height of 6 m . The width of the locks is 1 0 m . Lock A to B ( where the boat is moored ) 6 0 m long. The boat is 4 m...
Suppose one year T-bills current yield 5.95% in the future inflation rate is expected to be constant at 5.25% per year. What is the approximate real rate of return?
Binary Search Tree (14 points) Recall that in a binary search tree, each node is defined as follows. struct node { int key; node *left; node *right; node *parent; \ Other data *\ } Recall that in a...
If you look at stock prices over any year, you will find a high and low stock price for the year. Instead of a single benchmark PE ratio, we now have a high and low PE ratio for each year. We can use...
Different lamps might have batteries connected in either of the two arrangements shown in Fig. 18-33. What would be the advantages of each scheme? (b) (a)
In the simple quantity theory of money, what will lead to an increase in aggregate demand? In monetarism, what will lead to an increase in aggregate demand?
What and who is the U.S. government attempting to protect in its effort to preserve and regulate competition?
For each of the major laws discussed in the text, indicate whether in the long run the law will promote or restrict competition. As a consumer without any financial interest in business, what is your...
Drawing on data in Exhibit 3-4, do you think that Romania would be an attractive market for a firm that produces home appliances? What about Finland? Discuss your reasons.
The Cost of Goods Sold (COGS) for a manufacturing unit in 2020 was $150 million. The manufacturing units beginning and ending inventories were $20 million and $4 million respectively. What is the...
Explain what happened with the joint tenancy with right of survivorship. Who owns what now? Does Countrywide have a mortgage? Are Troy and Judy liable for the mortgage? Is their property subject to...
Alaska Airlines employed Tellis in Seattle as a maintenance mechanic. His wife was having difficulties with her pregnancy, so on the morning of July 4, 2000, he told his supervisor he needed to take...

Consider two operators (mathbf{A}) and B. Show that [e^{-i mathbf{A}} e^{-i mathbf{B}}=e^{-i(mathbf{A}+mathbf{B})}] only if (mathbf{A}) and (mathbf{B})

Question:

Step by Step Answer:

An Introduction To Groups And Their Matrices For Science Students

Students also viewed these Business questions