Page 41 - Trends in Science and Technology fo Sustainable Living

2 Fakultas Sains dan Teknologi
Universitas Terbuka (2023)

operator dan analisis fungsional. Tujuan penulisan artikel ini adalah
untuk mengkaji aljabar-C* serta penerapannya dalam mekanika
kuantum, khususnya terkait teorema spektral untuk operator-
operator self-adjoint tak terbatas di ruang Hilbert. Pada artikel ini,
dibahas terlebih dahulu beberapa teori dasar aljabar-C* termasuk
operator linear, operator adjoint, operator uniter, dan sifat-sifat
dasar lainnya yang terkait dengan teori mekanika kuantum.
Selanjutnya, pembahasan aljabar-C* dikerucutkan pada operator
self-adjoint tak terbatas di ruang Hilbert dengan memanfaatkan
transfromasi Cayley sehingga diperoleh teorema spektral untuk
operator tak terbatas dari operator terbatas. Selain itu, dijelaskan
pula penerapan Aljabar-C* dalam mekanika kuantum.

Kata Kunci: aljabar-C*, mekanika kuantum, operator self-adjoint,
teorema spektral.

ABSTRACT

In an era of increasingly developing technology, technological
innovation is carried out to achieve Sustainable Development
Goals (SDGs), which lead to sustainable living. Sustainable living
emphasizes the importance of wise use of natural resources,
environmental protection, reduction of waste and pollution, use
of renewable energy, awareness of social and economic impacts,
and individual and societal actions to achieve the SDGs' goals. In
this case, Mathematics is used to build mathematical models that
support analysis and planning related to SDGs goals, including
cryptography and quantum computers, which are closely related
to quantum mechanics. Mathematical concepts, especially C*-
algebra, can be used to analyze and model quantum systems
and related phenomena in quantum mechanics. Algebra-C* is
the result of a further study of the concepts of algebraic operators
and functional analysis. This article aims to study C*-algebra and
its application in quantum mechanics, particularly regarding the
spectral theorem for infinite self-adjoint operators in Hilbert space.