Question: Let the eigenfunctions and eigenvalues of an operator be {n} and {an}, respectively, so that A a n n n . Assume that the function

Let the eigenfunctions and eigenvalues of an operator be {n} and {an}, respectively, so that A a n n n . Assume that the function f(x) can be expanded in a Taylor power series expansion. Show that n is also an eigenfunction of f() with an eigenvalue f(an). That is, n n n f A f a

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

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 Mathematics Questions!

3.16 Let the eigenfunctions and eigenvalues of an operator be {p} and {a}, respectively, so that Apn = ann Let the function f(x) have the expansion f(x) = bx 1=0 Show that is an eigenfunction of...

ttth Suppose that the sequence of bags {Bn | n N} is recursively enumerated by the computable function e(n, x) = fn(x), [7 marks] Hence prove that the set of all recursive bags cannot be recursively...

1 2.3 Definition of a Discrete Probability Function Definition: Let S be a discrete sample space from some experiment. A function P, defined on all events in S, is said to be a probability function...

Exercises Chapter 2 2.1 Marginal and conditional probability: The social mobility data from Section 2.5 gives a joint probability distribution on (Y1 , Y2 )= (father's occupation, son's occupation)....

Math\t107-6381\t-\tQuiz\t#4\t-\tSchultz\t-\tDue\tFebruary\t21,\t2016\t-\tpage\t1\tof 3 Follow\tthese\tdirections\tcarefully. This\tquiz\tis\tdue\tby\t11:59\tEastern\ttime\ton\tFebruary\t21,\t2016. o...

GSB 420 Math Chapter 1-2 Calculus (Week1 In-Class Homework) Name : ______________________ I. Find X from the following equations (0.5 point each) 1. 3x = 90 2. Ln(ex) = 25 3. Monthly payment (X) of...

All questions. 05:50:42 VA; 25% ' ASSIGNMENTNM1.pdf IQ 0+ Numerical Methods-Assignment-l Mathematical Prelimanaries, Taylor's Theorem, Order of Convergence (1) Let L be a real number and let {an} be...

Help in solving this problem.k 6. (10) Consider the discrete time monetary-search model we saw in class. As in the baseline model, in the day time trade takes place in a decentralized market...

Math 105 Midterm Exam Review 1. A company will sell N(x) printers after spending x thousand dollars on advertising as modeled by the function N ( x) = 60x - x 2. a) Find the average rate of change of...

Hello can someone help Question 1 A delegation of three is to be chosen from the untenured faculty of the MIT Economics Department (numbering ten) to represent the department in an Institute-wide...

An investor has $1000 initial wealth for investment and he borrows another $1000 at the risk free rate. He then invest the entire total amount of $2000 in the market portfolio. What is his portfolio...

Which situation BEST describes PEA?

Your friend Sam, mistakenly wrote down the multiples of 1 0 as: 1 ; 2 ; 5 ; and 1 0 . Write down word for word how you will explain to Sam that those are not correct and how he should go about to...

When answering questions 16 through 23, assume that on August 1, 2022 a customer purchased a gift card from Best Buy. The customer paid cash of $50, and then gave the card to a friend. On August 20,...