Abstract
The concept of the effective mass in crystals shows that the electron mass is affected by the crystal field and was experimentally verified. A useful expression for effective mass was obtained. Unfortunately this expression showed that the effective mass vanishes in the ab-sence of the external field. This is in conflict with observations which show that it reduces to the ordinary mass. To cure this defect a new model is developed assuming the existence of vacuum force as verified experimentally as shown by Casimir effect. Using Newton’s second law and the quantum expression of momentum, useful expressions were found. The same expression was found using generalized special relativity. Strikingly the three models reduced to the conventional one in the absence of vacuum, they also reduced to the ordinary electron mass in the absence of all forces.
Highlights
Material science is one of the most important branches of physics
The quantum laws and Newton laws are used to construct a model which uses the concept of vacuum force, to prove that the effective mass reduced to the ordinary mass without any need of introducing the notion of external force
Using the Newtonian and quantum expressions of momentum and its relation with the force (1 - 5), a new simple derivation has been used to derive the conventional expression of the effective mass (9)
Summary
Material science is one of the most important branches of physics. It is concerned with the physical properties of matter to be utilized in modern technology [1]. These properties include electron mobility, diffusion, electric and magnetic interaction, besides the electron response to thermal energy and collision process [5]. The quantum laws and Newton laws are used to construct a model which uses the concept of vacuum force, to prove that the effective mass reduced to the ordinary mass without any need of introducing the notion of external force. This means that one needs to modify this relation to cure this defect
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