Calculating Effective Mass for a Free Electron: Homework Solution and Equations

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SUMMARY

The effective mass of a free electron can be calculated using the dispersion relation equation, specifically ε = ħ²k² / 2me. By substituting this expression into the effective mass formula, one can derive the effective mass directly. The relationship between energy and momentum in this context simplifies the calculation, confirming that the effective mass is equivalent to the actual mass of the electron, me, in free space.

PREREQUISITES
  • Understanding of quantum mechanics principles
  • Familiarity with the concept of dispersion relations
  • Knowledge of effective mass in solid-state physics
  • Basic proficiency in mathematical manipulation of equations
NEXT STEPS
  • Study the derivation of effective mass in semiconductor physics
  • Explore the implications of effective mass on electron mobility
  • Learn about the role of effective mass in band structure calculations
  • Investigate the differences between effective mass and rest mass
USEFUL FOR

Physics students, materials scientists, and anyone studying solid-state physics or semiconductor theory will benefit from this discussion.

raintrek
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Homework Statement



Calculate the effective mass for a free electron.

Homework Equations



44fe609850705ab89d76fc0714b65a4c.png


The Attempt at a Solution



I know the above equation comes from, in the case of the free electron dispersion relation,
1632e523513112a5ba15209fd3e8de9b.png
.

However I'm not at all sure how to go about calculating it for a free electron, given that the two formulae are basically one in the same...
 
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Note the following minor correction: the free electron dispersion relation is [itex]\epsilon = \hbar ^2 k^2 /2m_e[/itex]. What happens when you plug this into the expression for the effective mass?
 

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