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Homework Help: Effective mass

  1. Nov 23, 2016 #1
    1. The problem statement, all variables and given/known data
    1. For a simple cubic lattice with a lattice constant of a, the energy band can be expressed as:E = Acos(kxa)cos(kya)cos(kza) + B.

    (a) Suppose the effective mass for the electron at conduction band is m* = -ħ2/2a2, find A.

    2. Relevant equations

    3. The attempt at a solution
    I know the effective mass equation and how the effective mass tensor is calculated, but I can't really see how does the effective mass appear to be as indicated(m* = -ħ2/2a2).

  2. jcsd
  3. Nov 23, 2016 #2

    Dr Transport

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    What is the definition of the effective mass??? it isn't an extremely complicated expression...
  4. Nov 24, 2016 #3
    I think it's m* = ħ2/(∂2E/∂k2).
    but how am I going to use this?
    there are three components of k, and I'm not sure how to combine the three masses.

    Thanks for the reply.
  5. Nov 24, 2016 #4

    Dr Transport

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    you have the expression for E, do the derivatives, the effective mass will be anisotropic.....
  6. Nov 24, 2016 #5
    Thanks, I've done the derivatives, but the result is a tensor(shouldn't it?).

    how should I relate this with the single value provided by the question (m* = -ħ2/2a2)?
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