Question: For the wave functions n (x) = 2/L sin(nx/L) corresponding to a particle in an infinite square well potential from 0 to L, show

For the wave functions ψ_n(x) = √2/L sin(nπx/L) corresponding to a particle in an infinite square well potential from 0 to L, show that∫ ψ_n(x) ψ_m(x)dx = 0, that is, ψ_n and ψ_m are orthogonal.

Step by Step Solution

★★★★★

3.36 Rating (171 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

We need to show that The product of the two sine functions can be rewritten as the sum o... 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)

10-P-L-O-S-E (26).docx

120 KBs Word File

Students Have Also Explored These Related Light and Optics Questions!

A particle in an infinite square well makes a transition from a higher to a lower energy state; the corresponding energy decrease is 33 times the ground-state energy. Find the quantum numbers of the...

An electron is trapped in an infinite square well 25 nm wide. Find the wavelengths of the photons emitted in these transitions: (a) n = 2 to n = 1; (b) n = 20 to n = 19; (c) n = 100 to n = 1.

(a) For the wave functions corresponding to a particle in the nth state of a one-dimensional box of length L, show that (b) Compare this result for n >> 1 with your answer for the classical...

Question: 2. Consider a particle in an infinite square well. It is in the initial state y(x, 0) = A [$1(x) + $2(x)] where on (x) is the energy eigenfunctions for the infinite square well. (a) Plot...

A particle in an infinite square well V(x) = 0 for O S x Sa co for x a has, at time t = 0, the wave function P (x,0) = y(x) = A (3 sin (xx/a) - sin (4xx/a)). a. Write P (x,0) = y (x) as a linear...

The wave functions of a particle in a one-dimensional infinite square well are given by Equation 6-32. Show that for these functions n (x) m (x) dx = 0, that is, that n (x) and m (x) are...

A particle in an infinite square well V(x) = So for 0 5 x Sa co for x a has a normalized wave function that is an even mixture of its two first stationary-state eigenfunctions: P(x, 1 ) = A y(x)e in...

A particle in an infinite square well V ( x ) = 0 for O S x Sa oo for x a has a normalized wave function that is an even mixture of its two first stationary-state eigenfunctions: P ( x, 1 ) = A...

Edgar has died, and leaves a will that disposes of his property, giving all of it to his grandson David. Edgar's other grandson, Paul, had been taking care of Edgar for several years before his...

= n a X 2 n 2 2 EnE 2 ma3. ( /24 pts) Suppose an infinite square well potential is given by c D (a) (4 pts) Sketch the potential. (b) (12 pts) As we saw in class, the general solution to the infinite...

The equilibrium equations and Ka values for three reaction systems are given below. a. Which conjugate pair would be best for preparing a buffer with a pH of 2.88? H3O (a)HC204 (aq): Ka 5.6 X 10 H3O...

The accounting profession is concerned about whether companies are in compliance with various federal and state environmental laws and regulations and whether they have reported environmental...

1. Calculate the annual cost of each of the three accounts, assuming that Amys banking habits remain the same. Which plan would you recommend and why?

OnDecember 31 2007, Karmansky Company needed to record its accrued wages for year-end. December 31 is a Tues, and Karmasky Company must account for two days of wages. The company operates on a...

Archer Co. allows select customers to make purchases on credit. Its other customers can use either of two credit cards: Commerce Bank or Aztec. Commerce Bank deducts a 3% service charge for sales on...

A recent directive from Laura Jensen, CEO of Hermantown Manufacturing, had instructed each department to cut its costs by 15%. The traditional functional budget for the shipping and receiving...

Daniel Merrill is the manager of an airport gift shop, Merrill News and Gifts. From the following data, Mr. Merrill wants a cash budget showing expected cash receipts and disbursements for the month...

Blake and Anna Carlson are preparing a plan to submit to venture capitalists to fund their business, Music Masters. The company plans to spend $380,000 on equipment in the first quarter of 20X7....

Solve the Initial Value Problem. dy dt - t = 1 +y +ty, y(1) = 0

A point charge q moves uniformly and rectilinearly with a relativistic velocity equal to a fraction of the velocity of light ( = v/c). Find the electric field strength E produced by the charge at the...

At the moment t = 0 an electron leaves one plate of a parallel-plate capacitor with a negligible velocity. An accelerating voltage, varying as V = at, where a = 100 V/s, is applied between the...

A proton accelerated by a potential difference V gets into the uniform electric field of a parallel-plate capacitor whose plates extend over a length l in the motion direction. The field strength...

Global Technology's capital structure is as follows: \ table [ [ Debt , 5 0 8 ] , [ Preferred stock, 3 5 ] , [ Common equity, 1 5 ] ] The aftertax cost of debt is 8 . 5 0 percent; the cost of...

Queen B Corp. has a current annual cash dividend policy of $3.00. The price of the stock is set to yield 10% return. What is the price of this stock today if the dividend will be paid for 10 year and...

Excess reserves of commercial banks which are deposited with Federal Reserve Banks are referred to as: (A) discount funds (B) certificates of deposit (C) excess equity funds (D) federal funds