1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 1-D infinite potent. well

  1. Oct 29, 2009 #1
    Ok, I have a 1-D box confined at at x = 0 and x = L. So, points between 0 and L distances are the continuum state and otherwise distances be discontinous.
    a) I need to find the egien functs: Un(x) and related egien values: En .... n are the excited levels represented as postive whole numbers.

    The wave funct is: φ(x, t = 0) = (1/(3^1/2))U_2(x) + ((2/3)^1/2)U_3(x)

    b) As time progresses, what will the function look like?
    c) What is the prob. density (φ squared) and P(x,t) = total probability.

    What I have so far...

    (-(h/2pi)^2)/2m * (d^2/dx^2)Psi(x) = E*Psi(x)
    Psi(x)|x=0 = Asin(0) + Bcos(0) = B = 0 ?
    Psi(x)|x=L = Asin(kL) + Bcos(kL) = 0 ?

    [0 0; sin(kL) cos(kL)] *[A;B] = [0 0]

    set KnL/2 = n*pi
    En = (h/2pi)^2 *k^2]/2m
    = [(h/2pi)^2] /2m * (2n*pi/L)
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Nov 2, 2009 #2
  4. Nov 2, 2009 #3
    Hi Panic_Attack!

    In the second boundary condition you made a mistake, because you
    already know that B=0, You really have:

    [tex]\Psi(x=L) = ASin(kL) = 0 [/tex]

    And this condition say to you:

    [tex] kL = n\pi [/tex]


    [tex] k^{2}\equiv\frac{2mE}{\hbar^{2}} [/tex]

    Then you got [tex]E_{n}[/tex]

    To find the wave function you don't know A yet, but try to normalize the wave function.

    On (b) part.. Have you heard about the Evolution Operator? Maybe this simplify your problem.

    (Sorry my english sucks)
    Last edited: Nov 2, 2009
  5. Nov 5, 2009 #4
    Thanks so much for replying to my question. Fortunately I was able to find an answer without using the evolution operator. I basically went through solving with the schrodinger equation with setting up the solutions of the differential equations based on the regions. And had the same K value you got too. Then I normalised the wave function with it squared over the integral and found A too... I really apreciate your help, sorry I couldnt reply sooner.

    Your english sounds better than mine!! lol
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook