Importance of Hilbert Space In Quantum Mechanics

Ashoke Das; Sahin Injamamul Islam

doi:https://doi.org/10.14445/22315373/IJMTT-V66I1P512

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 66 | Issue 1 | Year 2020 | Article Id. IJMTT-V66I1P512 | DOI : https://doi.org/10.14445/22315373/IJMTT-V66I1P512

Importance of Hilbert Space In Quantum Mechanics

Ashoke Das, Sahin Injamamul Islam

Abstract

In this paper we have discussed about the importance of Hilbert space in Quantum Mechanics.Hilbert space has many applications in various field but in Quantum Mechanics Hilbert space is a vital component that can be denoted as the complete space of Inner product.Hilbert space plays a central role to integrate and determine the interpretation of Wave func- tion.We have been seen that for determining the material's electronic structure has used the atomic position.However,the implementation of the particular molecules delivers the accurate information of the change in vector position. A specific linear operator can be defined within all of the Hilbert space,it can be said that both are necessarily bounded.

Keywords

Hilbert Space,Quantum Mechanics,Wave function,Atomic Position,Orthonormal

References

[1]Arqub, O. A., Mohammed, A.S.,Momani, S., Hayat,T. (2016). Numerical solutions of fuzzy differential equations using reproducing kernel Hilbert space method.Soft Computing, 20(8), 3283-3302.
[2]Artacho, E., O'Regan, D. D. (2017). Quantum mechanics in an evolving Hilbert space. Physical Review B, 95(11), 115155.
[3]Cao, C., Carroll, S. M., Michalakis, S. (2017). Space from Hilbert space: recovering geometry from bulk entanglement.physical Review D, 95(2),024031.
[4]Celeghini,E.,Gadella,M., del Olmo,M.A.(2016).Applications of rigged Hilbert spaces in quantum mechanics and signal processing. Journal of Mathematical Physics, 57(7)072105.
[5]De-Ronde,C.(2015).Hilbert Space Quantum Mechanics isContextual (Reply to RB Griffiths). arXiv preprint arXiv:1502.05396.
[6]Dougherty, M. R., Slevc, L. R., Grand, J. A. (2019). Making research evaluation more transparent: Aligning research philosophy, institutional values, and reporting. Perspectives on Psychological Science, 14(3), 361-375.
[7]Fano, G., Blinder, S. M. (2017). Twenty-First Century Quantum Mechanics: Hilbert Space to Quantum Computers. Berlin: Springer.
[8]Giddings,S.B.(2015).Hilbert space structure in quantum gravity:an algebraic perspective. Journal of High Energy Physics, 2015(12), 1-21.
[9]Kanschat,G.(2019).Finite Elements.Retrieved from:https://simweb. iwr.uni-heidelberg.de/ gkanscha/notes/fem.pdf
[10]Lin, Y., Gaebler, J. P., Reiter, F., Tan, T. R., Bowler, R., Wan, Y., . Srensen, A. S. (2016). Preparation of entangled states through Hilbert space engineering. Physical review letters, 117(14), 140502.
[11] L.Debnath,P.Mikusinski,1980,Introduction to Hilbert space with Applications,Academic press,INC,New York,Toronto.
[12]Marcucci,G., Conti,C.(2016).Irreversible evolution of a wave packet in the rigged-Hilbert-space quantum mechanics.Physical Review A,94(5),052136.
[13]math.utoronto.ca(2019).Hilbert Spaces:An Introduction.Retrieved from:http://www.math.utoronto.ca/almut/MAT1001/SS3-Chapter4.pdf
[14]Osintseva, N. D., Choporova, Y. Y., Kameshkov, O. E., Knyazev, B. A., Pavelyev, V. S. (2018). Vector and mixed beams with orbital angular momentum. In EPJ Web of Conferences (Vol. 195, p. 07005). EDP Sciences.
[15]Perez Ortiz,R., Vlasov, V.V.(2016). Correct solvability of Volterra integrodifferential equations in Hilbert space.Electronic Journal of Qualitative Theory of Differential equation,2016(31),1-17
[16]quantum.phys.cmu.edu(2019).Hilbert Space Quantum Mechanics. Retrieved from:http://quantum.phys.cmu.edu/QCQI/qitd114.pdf
[17]Saglam,Z., Saglam, M.(2016).Canonical Angular Momentum of Electron, 10 Positron and the Gamma Photon.Journal of Modern Physics, 7(01), 134.
[18]Schlederer,F.,Krenn,M.,Fickler,R. Malik,M.and Zeilinger,A.,2016. Cyclic transformation of orbital angular momentum modes. New J.Phys, 18, p.043019.
[19]Strang,K.D.(2015).Matching research method with ideology and strategy.In The Palgrave Handbook of Research Design in Business and Management(pp.47-62).Palgrave Macmillan,New York.
[20]Walliman,N.(2017).Research methods:The basics.Abingdon:Routledge

Citation :

Ashoke Das, Sahin Injamamul Islam, "Importance of Hilbert Space In Quantum Mechanics," International Journal of Mathematics Trends and Technology (IJMTT), vol. 66, no. 1, pp. 92-102, 2020. Crossref, https://doi.org/10.14445/22315373/IJMTT-V66I1P512