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Shrodinger Equation help

  1. Feb 10, 2007 #1
    1. The problem statement, all variables and given/known data
    A particle of mass m in confined in a 1 dimensional box with origin at the center. the box extends from -a/2 to a/2 the potential energy is v(x) = 0 where -a/2<x< a/2 and infinite when x > a/2.

    I have to write the shrodinger equation for the outside and inside of the box, solve the equation for inside the box in the form of wavefunc = A sin (cx) + B cos (cx). Give a rule determining all possible values of C and for each possible c determined give the conditions the constants A and B must adhere to to make the wavefunction a satisfactory solution to the shrodinger EQ

    and last but not least express the energy in terms of C.


    2. Relevant equations

    H psi = E psi
    h bar (used down below) = h/2pi
    edit: oh i also used L instead of a for a variable when talking about the length of the box
    3. The attempt at a solution

    S.E. for particle outside box

    psi(x) = sqrt(2/L) sin (n pi x)/L

    S.E. for particle inside box

    (-h bar^2)/2m + d psi/dx^2 = i(h bar) d psi/dt


    solution to S.E for particle inside a box

    Psi (x,t) = Ae^(i2pi/lamda - omega t) ==== Ae^(ikx - iwt)

    ====
    solution using Eulers' rules
    Acos(kx - wt) + iAsin (kx-wt)


    are these answers right for above questions? or do the answers have to be more specific, i dont know im new to all this.

    ok when they ask to give a rule that determines all possible values of c what does that mean? this might seem dumb but im not even sure what c is.


    i registered for this forum specifically because im having alot of trouble in biophysical chem class, if anyone wants to help me it would be great.
     
  2. jcsd
  3. Feb 10, 2007 #2
    ooh and i can post any work leading up to the answers in the answer section but I refrained because i'm pretty sure my notation is horrible.
     
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