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|Title: ||Yet another position-dependent mass quantum model|
|???metadata.dc.creator???: ||Lima, Jonas Romero Fonseca de|
Vieira, Marcelo da Silva
Furtado, Claudio Benedito Silva
Moraes, Fernando Jorge Sampaio
|Publisher: ||American Institute of Physics|
|Issue Date: ||2012|
|Citation: ||LIMA, J. R. F. de et al. Yet another position-dependent mass quantum model. Journal of Mathematical Physics, New York, v. 53, p. 072101, 2012.|
|Abstract: ||The quantum dynamics of particles with mass dependent on the position is a problem
of interest since the effective-mass approach to charge carriers in conductors and
semiconductors began to be used. These problems have been solved using the Hamiltonian
H = 1
2mα(x)pmβ (x)pmα(x), where α and β are real parameters which satisfy
the condition 2α + β = − 1. It has been verified that the choice α = 0, β = − 1
is compatible with Galilean invariance. In this work we propose a new Hamiltonian,
Hˆ = 1
−1 pˆ2 + pˆmˆ (xˆ)
−1 pˆ + p2mˆ (xˆ)
, to describe variable mass systems.
We considered every permutation among the operators, taking into account that the
mass is now an operator. We verified that this Hamiltonian is Hermitian and is compatible
with Galilean invariance. For comparison, we used both Hamiltonians to
calculate the band structure for a quantum particle with mass varying periodically.
Although qualitatively equivalent, the results turn out to produce different numerical
|Appears in Collections:||DFI - Artigos publicados em periódicos|
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