Solving for A in a Simple Cubic Lattice

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Homework Statement


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.

Homework Equations

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).

Thanks!
 
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What is the definition of the effective mass? it isn't an extremely complicated expression...
 
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.
 
you have the expression for E, do the derivatives, the effective mass will be anisotropic...
 
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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