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Homework Help: Arithmetic Question Involving Quantum Physics

  1. Apr 23, 2014 #1
    1. The problem statement, all variables and given/known data

    Two adjacent allowed energies of an electron in a one-dimensional box are 2.0 eV and 4.5 eV. What is the length of the box?

    2. Relevant equations


    3. The attempt at a solution

    My question is, since E_n and n^2 are both on separate sides of the equation in the numerator, why can't I put Delta in front of each of these variables and solve for L?

    [tex]\Delta E_n=\frac{h^2\Delta n^2}{8mL^2}[/tex] and since the energy levels are adjacent, [tex]\Delta n^2=1[/tex]

    I tried doing this, but it gave me the incorrect answer. I know how I am supposed to do the problem now, I am just wondering why my original technique does not work.

  2. jcsd
  3. Apr 23, 2014 #2


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    Homework Helper

    Delta is shorthand for small change; essentially a derivative.
    when you change n^2 to (n+1)^2 , it is not really a small change,
    and clearly the change in the second depends on n.
    (that is, 1^2 is 1, but 2^2 = 4 ... a difference of 3
    5^2 = 25 , but 6^2 = 36 ... a difference of 11 , which is 3½ times as much.
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