Question: Let A and B be observables. Suppose the simultaneous eigenkets of A and B {|a, b} form a complete orthonormal set of base kets. Can

Let A and B be observables. Suppose the simultaneous eigenkets of A and B {|a′, b′〉} form a complete orthonormal set of base kets. Can we always conclude that [A, B] = 0?

If your answer is yes, prove the assertion. If your answer is no, give a counterexample.

Step by Step Solution

★★★★★

3.49 Rating (162 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

No we cannot always conclude that A B 0 based on the fact that the simultaneous eigenkets of A and B ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Modern Quantum Mechanics Questions!

Let A and B be oversvables, suppose the simultaneous eigenkets of A and B {|, b>} form a complete orthonormal set of base kets. Can we always conclude that [A, B] = 0? If your answer is yes, prove...

Let A and B be m x n matrices. (a) Suppose that vTAw = vT B w for all vectors v, w. Prove that A = B. (b) Give an example of two matrices such that vT A v = vT B v for all vectors v, but A B.

Let A and B be n ( n orthogonal matrices. (a)Prove that A (AT + BT)B = A + B. (b)Use part (a) to prove that, if det A + det B = 0, then A + B is not invertible.

Write an alternative definition that is tail-recursive (iterative) and makes use of accumulator variables. [10 marks] Explain why your alternative definition executes more efficiently. [3 marks] 1...

HW 12, MAT 312/AMS 351: SPRING 2017 Problem 1. (1) Set H = {4a + 6b | a, b Z} Z. Show that H is a subgroup of Z. (2) Is H cyclic? Problem 2. Write down all the cyclic subgroups of the following...

3 ,,uoh "gram 3 Eww 3 m T mm H a 3 .2 ' m w .,.m.av>v 3. m. @3on we geonwoaoa mm H "with M'nr H E. wads + we A at. ES 0 3.8V WEE 3563 mo wow 23 E m \"9H .3 avgmeMm\" mnemagouom Aggy\"...

Set Student Name: 1. Describe the relationship between two variables that have a correlation coefficient value: a. Near -1 b. Near 0 c. Near 1 2. Data was collected where a weightlifter was asked to...

Instuctor's Annotated Edition TENTH EDITION Understandable Statistics Concepts and Methods Charles Henry Brase Regis University Corrinne Pellillo Brase Arapahoe Community College Australia Brazil...

Set Student Name: 1. Answer true or false for each part, and if false, explain your answer. a. The point estimate for the population mean, , of an x distribution is x-bar, computed from a random...

From the book Networks, Crowds, and Markets: Reasoning about a Highly Connected World. By David Easley and Jon Kleinberg. Cambridge University Press, 2010. Complete preprint on-line at...

Levi McArthur graduated with a master of accountancy degree and has accepted a staff accounting position with a firm; he will receive a salary of $ 50,000. The firm guarantees that Levi will receive...

Suppose Pr(cell is 0 day old) = 0.4 Pr(cell is 1 day old) = 0.3 Pr(cell is 2 days old) = 0.2 Pr(cell is 3 days old) = 0.1. Consider again the cells in Section 6.4, Exercises 31 and 32, but suppose...

( a ) DNA sequences have four possible bases: C G A T . Below is an example of a part of a DNA sequence is shown. GATCCTCCAT ATACAACGGT ATCTCCACCT CAGGTTTAGA TCTCAACAAC GGAACCATTG ( i ) Consider an...

Your customer wants to develop a system for stock information where dealers can access information about companies and can evaluate various investment scenarios using a simulation system. Each dealer...

Prove [AB, CD] = AC {D, B} + A {C, B} D C {D, A} B + {C, A} DB. Discuss.

a. Consider two kets | > and | >. Suppose , , , | ), form a complete set of base kets. Find the matrix representation of the operator | >

Suppose | i > and | j > are eigenkets of some Hermitian operator A. Under what condition can we conclude that | i > + | j > is also an eigenket of A? Justify your answer.

Manipulation of Ratios and Ethical Behavior (Case 15-67) Pete Donaldson, president and owner of Donaldson Mining Supplies, was concerned about the firm's liquidity. He had an easy time selling...

E8-21 Journalizing transactions using the direct write-off method versus the allowance method During August 2018, Lima Company recorded the following . Sales of $133,300 ($122,000 on account $11,300...

Differentiate between a contract of service and a contract for service with examples.