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Cited article:

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The Schrödinger with variable mass model: mathematical analysis and semi-classical limit

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ON A DISCRETE MODEL FOR QUANTUM TRANSPORT IN SEMI-CONDUCTOR DEVICES

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PARITY-DECOMPOSITION METHOD FOR THE STATIONARY WIGNER EQUATION WITH INFLOW BOUNDARY CONDITIONS

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A discrete-velocity, stationary Wigner equation

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Journal of Mathematical Physics 41 (11) 7167 (2000)
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The One-Dimensional Wigner–Poisson Problem and Its Relation to the Schrödinger–Poisson Problem

H. Steinrück
SIAM Journal on Mathematical Analysis 22 (4) 957 (1991)
https://doi.org/10.1137/0522061