Hilbert space in quantum mechanics
Journal: Region - Educational Research and Reviews DOI: 10.32629/rerr.v6i7.2344
Abstract
Quantum mechanics is often considered as a relatively obscure physics course, which not only subverts beginners' cognition for Newton's motion laws in classical mechanics but also makes learners afraid, because of its complicated and profound mathematical theories in quantum mechanics. Thus, this article will, from the perspective of quantum mechanics, discuss the fundamental differences between the connotation of Hilbert space and spaces in classical mechanics. The application of Hilbert space in quantum mechanics will be expounded then. Finally, based on learners' difficulties existing in learning process, several teaching suggestions will be presented for future teaching reference.
Keywords
quantum mechanics; Hilbert space; physics; mathematics
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[5] Zeng JY. 2008. Quantum Mechanics Course. Beijing: Science Press.
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[7] Lyu CH. 2011. Development of quantum phase space theory using IWOP technique and entangled state representation. Hefei: University of Science and Technology of China.
[8] Lyu LQ, Jia CX, Wei GM, et al. 2006. Perturbation theory in quantum phase space. Chinese Journal of Molecular Sciences, 22(4): 231-237.
[9] Ivar F. 1903. Sur une elassed' equations fonctionnelles. Acta Mathematics, 27(1): 365-390.
[10] Li YY, Wang C. 2013. The origin of Hilbert space. Research on Dialectics of Nature, 29(12): 90-94.
[11] Wang QL, Li L. 2002. Operators and mechanical quantities in quantum mechanics. Journal of Xinjiang Normal University, 21(3): 19-23.
[12] Ning YL, Li CJ, Chen HJ, et al. 2018. On the difference between quantum mechanics and classical mechanics. Journal of Gansu Radio and Television University, 28(5): 83-86.
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