HILBERT SPACES AND THEIR APPLICATIONS IN QUANTUM MECHANICS

https://doi.org/10.5281/zenodo.14930665

Authors

  • Nurmanova Ezoza Ulugbek qizi Student of “Applied Mathematics” branch of Jizzakh National University of Uzbekistan Author
  • Khushvaqtova Diyora Shavkat qizi Student of “Applied Mathematics” branch of Jizzakh National University of Uzbekistan Author
  • Shokirova Hilola Farkhod qizi Student of “Applied Mathematics” branch of Jizzakh National University of Uzbekistan Author
  • Shodiyeva Sabina Dusmurod qizi Student of “Applied Mathematics” branch of Jizzakh National University of Uzbekistan Author

Keywords:

Hilbert spaces, quantum mechanics, Schrödinger equation, Fourier series, spectral properties, quantum harmonic oscillator, spin-1/2 systems, quantum teleportation, Pauli matrices, wave functions

Abstract

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.

References

.Dirac, P.A.M. The Principles of Quantum Mechanics. Oxford University Press, 1958.

.Griffiths, D.J. Introduction to Quantum Mechanics. Cambridge University Press, 2018.

.Sakurai, J.J. Modern Quantum Mechanics. Addison-Wesley, 1994.

.Reed, M., Simon, B. Methods of Modern Mathematical Physics, Vol. 1. Academic Press, 1980.

.von Neumann, J. Mathematical Foundations of Quantum Mechanics. Princeton University Press, 1955.

.Courant, R., Hilbert, D. Methods of Mathematical Physics. Wiley, 1989.

.Hall, B.C. Quantum Theory for Mathematicians. Springer, 2013.

.Ballentine, L.E. Quantum Mechanics: A Modern Development. World Scientific, 2014.

.Nielsen, M.A., Chuang, I.L. Quantum Computation and Quantum Information. Cambridge University Press, 2010.

.Thirring, W. Quantum Mathematical Physics: Atoms, Molecules and Large Systems. Springer, 2013.

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Published

2025-01-26

Issue

Vol. 1 No. 4 (2025): The Fourth International Scientific and Practical Conference

Section

Articles

License

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

How to Cite

Nurmanova , E., Khushvaqtova , D., Shokirova , H., & Shodiyeva , S. (2025). HILBERT SPACES AND THEIR APPLICATIONS IN QUANTUM MECHANICS: https://doi.org/10.5281/zenodo.14930665. International Scientific and Practical Conference, 1(4), 177-181. https://bestjournalup.com/index.php/ispc/article/view/1163