Unendlich-dimensionale Quantenwelt • Senkrechte Basis im Hilbert-Raum • vAzS (125) | Josef M. Gaßner

How can infinitely many functions be perpendicular to each other and form an orthonormal basis? In the series "From Aristotle to String Theory" (https://www.youtube.com/playlist?list..., Josef M. Gaßner demonstrates, using the Fourier basis, that sin(nx) and cos(mx) are pairwise perpendicular to each other for all n ≠ m and, through a suitable scalar product and normalization, form an infinite-dimensional orthonormal basis. This brings us full circle to the Fourier expansion from episode 123. This video is part of the playlist "From Aristotle to String Theory" Link to the playlist ►    • Von Aristoteles zur Stringtheorie   Big Bang, Universe and Life (www.urknall-weltall-leben.de) Scientists explain science Books related to the channel ► https://urknall-weltall-leben.de/shop... Live lectures ► https://www.josef-gassner.de/veransta... Donate ► https://urknall-weltall-leben.de/spen... Subscribe ► https://www.youtube.com/user/UrknallW... Thank you to everyone who supports our project!