Question: Evaluate the normalization integral for the eigenfunctions of H for the particle in the box n (x) = A sin(nx/a) using the trigonometric identity

Evaluate the normalization integral for the eigenfunctions of Hˆ for the particle in the box ψ _n (x) = A sin(nπx/a) using the trigonometric identity sin² y = (1 − cos2y)/2.

Step by Step Solution

★★★★★

3.46 Rating (172 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

1 4 sin 0 Let y a dx a a dx d... 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 Physical Chemistry Questions!

Are the eigenfunctions of H for the particle in the one-dimensional box also eigenfunctions of the momentum operator p x ? Calculate the average value of p x for the case n = 3. Repeat your...

Are the eigenfunctions of H for the particle in the one-dimensional box also eigenfunctions of the position operator x ? Calculate the average value of x for the case where n = 3. Explain your result...

The associated Legendre functions Pl|m| (w) are defined by Verify that P00(w) = 1, P01(w) = w, P11(w) = (1 - w2)1/2 and find P02(w), P12(w), and P22(w). It can be shown that (Pauling and Wilson, page...

questions below: Determine if the following vectors are orthogonal. 10 2 UE 5 V= 5 Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a simplified...

3-16. Show that (p) = 0 for all states of a one-dimensional box of length a. 3-21. Using the trigonometric identity sin a sin = 1 cos(- B) - cos(a + B) show that the particle-in-a-box wave functions...

10 Green's functions for PDEs In this final chapter we will apply the idea of Green's functions to PDEs, enabling us to solve the wave equation, diffusion equation and Laplace equation in unbounded...

Gaussian function variable Example 2-4 Gaussian function s(t) = (2.27) which is the standard Gaussian function with the mean time t, The Fourier trans- form is s(w) - Jamexp -"(t-1 ) expi-jothat =...

I. What I Know (Pre-Test) Instruction: Choose the letter of the correct answer to the following items. Write them on a separate sheet of paper. 1. If y = f(g(x)) where y = ese'x, choose f(x) such...

1 Express the area of the region bounded by the given line(s) and/or curve(s) as an iterated double integral. The curves and 5 points Question 2 Evaluate the integral. - - 5 points Question 3 Find...

please use this format filename 1 .. 10 name file 2 1 .. 10 Back Indefinite Integrals Graded Quiz - 30 min - 10 total points Due Sep 25, 11:59 PM WIB True or false? If the function f is continuous on...

8. Which sequential circuits generate the feedback path due to the cross- coupled connection from output of one gate to the input of another gate? a. Synchronous b. Asynchronous . Both d. None of the...

William Thompson was denied credit based on an inaccurate credit report compiled by the San Antonio Retail Merchants Association. The Association confused Thompsons credit history with that of...

3.3 A hotel group prepares financial statements on a quarterly basis. The senior management is reviewing the performance of one hotel and making plans for next year. The managers have in front of...

5-6 Meta-analysis is an important way to summarize the biomedical literature because they pull together information from many different studies to provide a quantitative estimate of the effect of a...

Why do the activity coefficients of ions in solution differ from 1? Why are they less than 1 in dilute solutions?

The mean activity coefficients for aqueous solutions of NaCl at 25 C are given opposite. Confirm that they support the DebyeHckel limiting law and that an improved fit is obtained with the Davies...

The following temperaturecomposition data were obtained for a mixture of octane (O) and methylbenzene (M) at 1.00 atm, where x is the mole fraction in the liquid and y the mole fraction in the vapour...

The Mini-Max Company has a new prospective 5-year project with an initial cost of $318,900, annual fixed costs of $45,200, variable costs per unit of $16.78, and a sales price of $29.95. The discount...

Locate the Treasury issue in Figure 7.4 ?maturing in February 2041. Assume a par value of $10,000. What is its coupon rate? (Enter your answer as a percent r ounded to 3 decimal places, e.g.,...

Suppose that a national survey finds that 73 percent of restaurant employees say that work stress has a negative impact on their personal lives. A random sample of 200 employees of a large restaurant...