Question: Two observables A1 and A2, which do not involve time explicitly, are known not to commute, [A1, A3] 0, yet we also know that

Two observables A1 and A2, which do not involve time explicitly, are known not to commute, [A1, A3] ≠ 0, yet we also know that A1 and A2 both commute with the Hamiltonian: [A1, H] = 0, [A2, H] = 0. Prove that the energy eigenstates are, in general, degenerate. Are there exceptions? As an example, you may think of the central-force problem H – P2/2m + v(r), with A1 → Lz, A2 → Lx.

Step by Step Solution

★★★★★

3.33 Rating (156 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

No degeneracy Implies in defined by Hn Ela is unique 16 only one e... 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

Document Format (1 attachment)

28-P-M-P-Q-M (162).docx

120 KBs Word File

Students Have Also Explored These Related Modern Physics Questions!

You may think of your college or university as an organization that offers a line of different educational products. Assume that you have been hired as a marketing consultant by your university to...

The nuclei involved in the nuclear reaction A1 + A2 A3 + A4 have the binding energies E1, E2, E3, and E4. Find the energy of this reaction.

Two parallel-plate vacuum capacitors have areas A1 and A2 and equal plate spacings d. Show that when the capacitors are connected in parallel, the equivalent capacitance is the same as for a single...

Applied Mathematics and Computation 95 (1998) 181192 Love dynamics: The case of linear couples Sergio Rinaldi 1 Centro Teoria dei Sistemi, CNR, Politecnico di Milano, Via Ponzio 34/5, 20133 Milan,...

chapter 5 INTRODUCTION TO MATRIX ALGEBRA GOALS The purpose of this chapter is to introduce you to matrix algebra, which has many applications. You are already familiar with several algebras:...

Algorithms in Artificial Intelligence (or, the old name: Introduction to Algorithmic Decision Making) Part 1 Based on slides by David Sarne and Lirong Xia Course Tentative Schedule Introduction...

Summarize the article.Next discuss,from the article's perspective,the customer's influence in the master scheduling process. Power Relationships and Schedule Flexibility: Case Studies on Two Supply...

BA 1605: Midterm Recap (Due: Feb. 27, 2015) Name _____________________________ 50 Student ID _____________________________ Section 01B 10:00~11:20 am Section 02B 01:00~02:20 pm [Questions 4 ~ 7] The...

from pages 5-39 of Stanford's Health Care Report- any particular point that feel may be relevant or interesting in regards to financial status current or future for Stanford. Has to be least 200...

Suzys Temporary Employee (STE) business, located in a big city, can do an on-line criminal background check in-house for $1.64 per search with a fixed cost of $24,000. A third party on-line security...

Andrew, age 65, is retiring and has 150,000 to invest. Andrew will not have any other substantial income, and he will be in the 15% marginal income tax bracket. He has invested in bonds in the past,...

1.10 What has been the Japanese contribution to operations management?

Use the Target Corporations Form 10-K to answer the following questions related to Targets 2012 fiscal year (year ended February 2, 2013). Targets Form 10-K is available on the companys website or...

The adjusted trial balance of Maytagg Repairs on December 31, 2011, follows. Required 1. Prepare an income statement and a statement of retained earnings for the year 2011, and a classified balance...

Use the Target Corporations Form 10-K to answer the following questions related to Targets 2012 fiscal year (year ended February 2, 2013). Targets Form 10-K is available on the companys website or...

The adjusted trial balance of University Book Store as of November 30, 2013, after the firm's first month of operations, appears on the next page. Appropriate adjustments have been made for the...

The adjusted trial balance of Reid and Campbell Ltd. at December 31, 2014, appears below. Requirements 1. Prepare Reid and Campbell Ltd.'s 2014 income statement, statement of retained earnings, and...

A 0.250-kg block of a pure material is heated from 20.0C to 65.0C by the addition of 4.35 kJ of energy. Calculate its specific heat and identify the substance of which it is most likely composed.

The Hamiltonian matrix for a two-state system can be written as Clearly, the energy eigenfunctions for the unperturbed problems ( = 0) are given by (a) Solve this problem exactly to find the energy...

A slightly anisotropic three-dimensional harmonic oscillator has z x = y . A charged particle moves in the field of this oscillator and is at the same time exposed to a uniform magnetic field in...

Evaluate the matrix elements (or expectation values) given below. If any vanishes, explain why it vanishes using simple symmetry (or other) arguments. [In (a) and (b), |nlm stands for the energy...

Let X1, . .., X30 be a random sample from a normal distribution with unknown mean / and known variance o = 3. Consider the following hypotheses: Ho : 1 = 1, H1 : / > 1. A sample @1, ..., @30 is...

(a) Overall, who gains and who loses? (b) What is the sum of gains and losses? (c) Anyone default in this futures example? Long is AAA Short is BBB \begin{tabular}{|c|c|c|} \hline Timet & Futures...

question 3 please 3. [CLO-3(C4)] A cardiac pacemaker is a medical device that generates electrical impulses delivered by electrodes to cause the heart muscle chambers to contract and therefore pump...