  Quantum mechanics is formulated as a geometric theory on a Hilbert manifold.
Images of charts on the manifold are allowed to belong to arbitrary Hilbert
spaces of functions including spaces of generalized functions. Tensor equations
in this setting, also called functional tensor equations, describe families of
functional equations on various Hilbert spaces of functions. The principle of
functional relativity is introduced which states that quantum theory is indeed
a functional tensor theory, i.e., it can be described by functional tensor
equations. The main equations of quantum theory are shown to be compatible with
the principle of functional relativity. By accepting the principle as a
hypothesis, we then analyze the origin of physical dimensions, provide a
geometric interpretation of Planck's constant, and find a simple interpretation
of the two-slit experiment and the process of measurement.
