{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

oldexam(3) - EE 439x Exam 1 Oct.18 2006 Name 1...

Info icon This preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
EE 439x Name_______________________________________ Exam 1 – Oct.18, 2006 1. Two-dimensional quantum well A two-dimensional, infinitely deep quantum well is defined by the potential U for x < 0, x > L x , y < 0, and y > L y . U = 0 for 0 < x < L x and 0 < y < L y . In 2-D, the Schroedinger equation takes the form " h 2 2 m # 2 $ x , y ( ) # x 2 " h 2 2 m # 2 $ x , y ( ) # y 2 + U x , y ( ) $ x , y ( ) = E $ x , y ( ) . Find the 2-D wave functions and corresponding energies for electrons trapped in this well.
Image of page 1

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

View Full Document Right Arrow Icon
EE 439x Name_______________________________________ Exam 1 – Oct.18, 2006 Half of a harmonic oscillator Consider a “half-harmonic-oscillator” potential, defined by U(x) = ½ kx 2 = ½ m ω 2 for x > 0 U(x) for x < 0 Thus, the potential has an infinite barrier at x = 0. Sketch the wave functions and determine the energies (in terms of ω ) for the two lowest states of this potential. V(x) x For reference the wave functions and energies for the 4 lowest states of the full harmonic oscillator (i.e. the one we did in class) are given below. -4 -3 -2 -1 0 1 2 3 4 ! 1 x 0 -4 -3 -2 -1 0 1 2 3 4 !
Image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    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.

    Student Picture

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

  • Left Quote Icon

    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.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    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.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern