Page 42 - Trends in Science and Technology fo Sustainable Living

Trends in Science and Technology 3
for Sustainable Living

In this article, we first discuss some of the fundamental theories
of C* algebra, including linear operators, adjoint operators, unitary
operators, and other essential properties related to the theory of
quantum mechanics. Furthermore, the discussion of C* algebra is
narrowed down to the infinite self-adjoint operator in Hilbert space
by utilizing the Cayley transform to obtain the spectral theorem for
the infinite operator of the finite operator. In addition, it also explains
the application of Algebra-C* in quantum mechanics.

Keywords: algebra-C*, quantum mechanics, self-adjoint operators,
spectral theorems