# hwsol8 - Physics 31 Spring 2008 Solution to HW#8 In region...

This preview shows pages 1–2. Sign up to view the full content.

Physics 31 Spring, 2008 Solution to HW #8 Problem A For this problem, you are to work out the so- lution for the wave function in a finite square well, for the case of an odd wave function. (In class, we did the case of an even wave function.) V = V 0 V = 0 x - L /2 0 + L /2 E I II (a) Write down the explicit form of the time-independent Schroedinger equation in region I. Let ψ I ( x ) = sin kx , where k 2 = 2 mE/ ¯ h 2 , and explain why this ψ I ( x ) is the desired solution to the Schroedinger equation. (b) Write down the explicit form of the time-independent Schroedinger equation in region II, and verify that ψ II ( x ) = C exp( αx ) + D exp( αx ) is a solution to this equation. What is α ? (c) Write down the equations for the continuity of the wave function and its derivative at the point x = L/ 2. Solve the equations to find the condition that must be satisfied in order to have C = 0. Explain why there is a physical solution only for certain values of the energy E . In region I, the Schroedinger equation is ¯ h 2 2 m d 2 dx 2 + 0 E ψ = 0 , where the 0 is the value of V ( x ) in region I. The general solution to this equation is ψ I ( x ) = A sin kx + B cos kx, where k 2 = 2 mE/ ¯ h 2 . In class we considered the even so- lutions and took the cosine term. Now we want the odd solutions, so we take the sine term. That is, we set A = 1 and B = 0, and we won’t worry about normalization.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern