HILBERT SPACES AND THEIR APPLICATIONS IN QUANTUM MECHANICS: https://doi.org/10.5281/zenodo.14930665 - Nurmanova , Ezoza; Khushvaqtova , Diyora; Shokirova , Hilola; Shodiyeva , Sabina (International scientific and practical conference, 2025)
This paper explores the concept of Hilbert spaces and their applications in quantum mechanics. First, the definition and properties of Hilbert spaces are analyzed, followed by an explanation of their use in quantum mechanics. Additionally, fundamental concepts of quantum mechanics, including wave functions and expectation value operators, are described in terms of Hilbert spaces. The paper also presents mathematical solutions to key applications of Hilbert spaces in quantum mechanics.