# PS3_v2 - Physics 115A Problem Set 3 Due Tuesday October 13...

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

Physics 115A, Problem Set 3 Due Tuesday, October 13 @ 5pm in the box outside Broida 1019 (PSR) Suggested reading: Griffiths 2.1-2.3 1 E and V for normalizable solutions Griffiths Problem 2.2: Show that E must exceed the minimum value of V ( x ), for every normalizable solution to the time-independent Schr¨ odinger equation. What is the classical analog to this statement? Hint: Rewrite Equation 2.5 in the form d 2 ψ dx 2 = 2 m ~ 2 [ V ( x ) - E ] ψ ; if E < V min , then ψ and its second derivative always have the same sign –argue that such a function cannot be normalized. 2 Initial States in a Box You prepare a particle in the infinite square well (with walls at x = 0 , a ) in an initial state described by a linear combination of two stationary states, Ψ( x, 0) = A [ ψ 1 ( x ) + ψ 3 ( x )] 1. Normalize Ψ( x, 0), i.e., find A . 2. Find Ψ( x, t ) and | Ψ( x, t ) | 2 . Express the latter as a sinusoidal function of time in terms of the variable ω = π 2 ~ / 2 ma 2 . 3. Compute h x i . Is this an interesting function of time? What happened to the time- dependent terms? Why? 4. Compute h p i . 5. If you measured the energy of the particle, what values might you get, and what is the probability of getting them? What is the expectation value of H

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