The Hilbert space L2 and its self adjoint linear operators in quantum mechanics - Agustito, Denik; Setyawan, Dhimas Nur; Sebastian, Rio; Erlangga, Sony Yunior; Trisniawati (Prodi Pendidikan Fisika Universitas Sarjanawiyata Tamansiswa, 2024)
This paper aims to explain the relationship between the concepts of state, position, and momentum in Quantum Mechanics and the mathematical objects in the study of Functional Analysis. The relationship between functional analysis and quantum mechanics is that if there is the notion of state space, momentum and position, then the relationship with functional analysis is that the state space forms a Hilbert space and momentum and position are seen as operators in the Hilbert space. The method used in this research is a literature review, which conducts a comprehensive review of literature, including textbooks and journals on functional analysis, operator theory, Hilbert spaces, and quantum mechanics. The results and conclusions of this study reveal that the state in Quantum Mechanics forms a class of all sets of square-integrable functions, represented by , which possesses the structure of a complex Hilbert space. Furthermore, Position and momentum in Quantum Mechanics are represented as self-adjoint linear operators on L2, a complex Hilbert space of square-integrable functions.