# Homework Help: Effective mass

1. Nov 23, 2016

### Josh1079

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).

Thanks!

2. Nov 23, 2016

### Dr Transport

What is the definition of the effective mass??? it isn't an extremely complicated expression...

3. Nov 24, 2016

### Josh1079

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.

4. Nov 24, 2016

### Dr Transport

you have the expression for E, do the derivatives, the effective mass will be anisotropic.....

5. Nov 24, 2016

### Josh1079

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)?