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Spin-polarized quantum well states on<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mtext>Bi</mml:mtext><mml:mrow><mml:mn>2</mml:mn><mml:mo>โ</mml:mo><mml:mi>x</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mtext>Fe</mml:mtext><mml:mi>x</mml:mi></mml:msub><mml:msub><mml:mtext>Se</mml:mtext><mml:mn>3</mml:mn></mml:msub></mml:mrow></mml:math>
Low temperature scanning tunneling microscopy is used to image the doped topological insulator ${\text{Bi}}_{2\ensuremath{-}x}{\text{Fe}}_{x}{\text{Se}}_{3}$. Interstitial Fe defects allow the detection of quasiparticle interference, and the reconstruction of the empty state band structure. Quantitative comparison between measured data and density functional theory calculations reveals the unexpected coexistence of quantum well states โฆ