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We calculate the effect of a spatially dependent effective mass (SPDEM) [adapted from Costa Filho et al. (2011)] on an electron and a hole confined in a quantum well (QW). In the work of Costa Filho et al., the translation operator is modified to include an inverse character length scale, γ , which defines the SPDEM. The introduction of γ means that translations are no longer additive. In nonadditive space, we choose a ‘skewed’ Gaussian confinement potential defined by the replacement x → γ − 1 ln ( 1 + γ x ) in the usual Gaussian potential. Within the parabolic approximation γ is inversely related to the QW thickness and we obtain analytic solutions to our confinement Hamiltonian. Our calculation yields a reduced dispersion relation for the gap energy ( E G ) as a function of QW thickness, D : E G ~ D − 1 , compared to the effective mass approximation: E G ~ D − 2 . Additionally, nonadditive space contracts the position space metric thus increasing the occupied momentum space and reducing the effective mass, in agreement with the relation: m o ⁎ − 1 ∝ ∂ 2 E / ∂ k 2 . The change in the effective mass is shown to be a function of the confinement potential via a point canonical transformation. Our calculation agrees with experimental measurements of E G for Si and Ge QWs. [ABSTRACT FROM AUTHOR]