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Quantum Well Solution

  1. Sep 24, 2007 #1
    I just took up my first course of quantum mechanics and i am having some serious problems solving quantum well problems.the thing is that after i take out the energy states of the well
    and try to find K1 and K2 from it, the values i get are very very large.i think i am making a msitake with units somewhere.here r the units that i am taking.can someone plz point out where im making a mistake.

    K1=sqrt(2*m*E/h^2)
    K2=sqrt(2*m*(V-E)/h^2)

    E=energy(i am converting ev to Joules)
    V=well depth(i am again converting ev to J)
    m=e mass(9.1e-31)
    h=1.054e-34 J.s
    all lengths in meters

    So if for example E=.245ev ,V=.36ev,what values of K1 and K2 should i be getting.

    Thanx
     
  2. jcsd
  3. Sep 24, 2007 #2
    Think about this. The thing that sets the scale at the quantum level is [tex]\hbar[/tex]. Your values for E and V are so much above this, that you should not be surprised to see large values for k.
     
  4. Sep 24, 2007 #3
    But im converting everything to SI units.Shouldnt that be right?
     
  5. Sep 24, 2007 #4

    malawi_glenn

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  6. Sep 24, 2007 #5
    this not a homework.just a question realted to Qm.the example i gave is just a random example.
     
  7. Sep 24, 2007 #6

    malawi_glenn

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    Well it looks very much as something that is in home work problems..It is just a question if you got the right order of magnitute. Whats related to Qm is quite much if we do this definition..

    And you should get something in the order of 10^9; what do you get?

    k1 = 2.53*10^9
    k2 = 1.74*10^9
     
  8. Sep 24, 2007 #7
    im getting the same thing but its not right.thats y i think im making the a mistake in the units.
     
  9. Sep 25, 2007 #8

    malawi_glenn

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    If this is a homework problem, post the original problem and as many steps as possible so that we may help you properly. Maybe you get wrong due to some other misstake in another part of the problem?

    It cant be wrong if you have mass in kg, energy in J and h-bar in J*s
     
  10. Sep 25, 2007 #9
    ok im posting an example from book.its slightly different but solving this wpild solbve my problem with units
    For a single quantum well
    K1=sqrt(2*m*E/h^2)
    K2=sqrt(2*m*(V-E)/h^2)

    aplpplying theb boundry conditions on the well gives us
    plot(1)
    k1=k2*tan(k2*a/2)
    -k1=k2*cot(k2*a/2)

    an additional relationship is obtained
    plot(2)
    k1^2+k2^2=*m*V/h^2

    which would be a circle.ploting the above would give me the k1 and k1 values at the points of intersection of the grfaph and from that i can find the values for E using the above realtion.

    if well width=a=10e-10m
    well depth=V=.347ev
    m=9.1e-31
    the ans is E1=.12660ev E2=.3413ev

    I cant get this answer!!
     
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