Mathematics Behind the Heisenberg Uncertainty Principle
DOI:
10.29303/jppipa.v9i4.3545Published:
2023-04-30Issue:
Vol. 9 No. 4 (2023): AprilKeywords:
Fourier series, Heisenberg uncertainty, Integral transform, Wave packetResearch Articles
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Abstract
Most physics books do not reveal clearly how the Heisenberg uncertainty principle was derived. This uncertainty comes from the consequence of the wave-particle duality of matter giving statement that position and momentum cannot be measured in the same time. This article tries to reveal mathematics background behind the expression the Heisenberg uncertainty using supported mathematics background such as Fourier transform, Fourier transform integral, the probability of Gaussian distribution and it ends up with the expression of wave function which describe the localized particle giving relation Heisenberg uncertainty principle.
References
Amico, M., & Dittel, C. (2020). Simulation of wave-particle duality in multipath interferometers on a quantum computer. Physical Review A, 102(3), 032605. https://doi.org/10.1103/PhysRevA.102.032605
Atalay, B., Jönsson, P., & Brage, T. (2023). Extended relativistic multiconfiguration calculations of energy levels and transition properties in singly ionized tin. Journal of Quantitative Spectroscopy and Radiative Transfer, 294(108392). https://doi.org/10.1016/j.jqsrt.2022.108392.
Bercioux, D., van den Berg, T. L., Ferraro, D., Rech, J., Jonckheere, T., & Martin, T. (2020). Wave-particle duality of electrons with spin-momentum locking. The European Physical Journal Plus, 135(10), 811. https://doi.org/10.1140/epjp/s13360-020-00837-3
Carnio, E. G., Breuer, H.-P., & Buchleitner, A. (2019). Wave–Particle Duality in Complex Quantum Systems. The Journal of Physical Chemistry Letters, 10(9), 2121–2129. https://doi.org/10.1021/acs.jpclett.9b00676
Carosso, A. (2022). Quantization: History and problems. Studies in History and Philosophy of Science, 96, 35–50. https://doi.org/10.1016/j.shpsa.2022.09.001.
Dalimier, E., & Oks, E. (2014). Analytical theory of charge-exchange-caused dips in spectral lines of He-like ions from laser-produced plasmas. Journal of Physics B: Atomic, Molecular and Optical Physics, 47(10), 105001. https://doi.org/10.1088/0953-4075/47/10/105001
Dani, A. T. R., & Adrianingsih, N. Y. (2021). Pemodelan Regresi Nonparametrik dengan Estimator Spline Truncated vs Deret Fourier. Jambura Journal of Mathematics, 3(1), 26–36. https://doi.org/10.34312/jjom.v3i1.7713
Dolce, D. (2023). Is time a cyclic dimension? Canonical quantization implicit in classical cyclic dynamics. Annals of Physics, 448, 169182. https://doi.org/10.1016/j.aop.2022.169182
Firman, H. (2019). Kepastian Dan Ketidakpastian Dalam Sains. Jurnal Filsafat Indonesia, 2(1), 33. https://doi.org/10.23887/jfi.v2i1.17549
Kaneyasu, T., Hikosaka, Y., Fujimoto, M., Iwayama, H., & Katoh, M. E. (2021). Electron Wave Packet Interference in Atomic Inner-Shell Excitation. Physical Review Letters, 126(11), 113202. https://doi.org/10.1103/PhysRevLett.126.113202
Kusuma, D. T. (2020). Fast Fourier Transform (FFT) Dalam Transformasi Sinyal Frekuensi Suara Sebagai Upaya Perolehan Average Energy (AE) Musik. PETIR, 14(1), 28–35. https://doi.org/10.33322/petir.v14i1.1022
Lyulin, O. M., Vasilchenko, S. S., & Perevalov, V. I. (2023). High sensitivity absorption spectroscopy of acetylene near 770 nm. Journal of Quantitative Spectroscopy and Radiative Transfer, 294(108402). https://doi.org/10.1016/j.jqsrt.2022.108402.
Pawly, J., Neitzel, R. L., & Basu, N. (2019). Analysis of copper, selenium, and zinc in newborn dried bloodspots using total reflection X-ray fluorescence (TXRF) spectroscopy. PeerJ Analytical Chemistry, 1, e1. https://doi.org/10.7717/peerj-achem.1
Pebralia, J. (2020). Prinsip Ketidakpastian Heisenberg dalam Tinjauan Kemajuan Pengukuran Kuantum di Abad 21. Journal Online of Physics, 5(2), 43–47. https://doi.org/10.22437/jop.v5i2.9049
Ray, A. (2023). Radiation effects and hardening of electronic components and systems: an overview. Indian Journal of Physics. https://doi.org/10.1007/s12648-023-02644-9
Ren, J., Qin, L., Feng, W., & Li, X.-Q. (2020). Weak-value-amplification analysis beyond the Aharonov-Albert-Vaidman limit. Physical Review A, 102(4), 042601. https://doi.org/10.1103/PhysRevA.102.042601
Riyani, A. N. E. S., Rizqiyah, P., & Junaidi, A. (2019). Mengidentifikasi Sinyal Suara Manusia Menggunakan Metode Fast Fourier Transform(FFT) Berbasis Matlab. J. of Insita, 1(2), 042–050. https://doi.org/10.20895/INISTA.V1I2
Rosdianto, H., & Toifur, M. (2017). Implementasi Teori Distribusi Probabilitas Gaussian pada Kualitas Rangkaian Penyearah Gelombang Penuh. Spektra: Jurnal Fisika Dan Aplikasinya, 2(1), 83 – 90. https://doi.org/10.21009/SPEKTRA.021.12
Salim, M. I., & Adnan Sauddin, M. I. N. (2022). Fourier Series Nonparametric Regression Model In The Case Of Open Unemployment Rate In South Sulawesi. Jurnal Matematika Dan Statistika Serta Aplikasinya, 10(2). https://doi.org/10.24252/msa.v10i2.30993
Sujito, S., Sunardi, S., Ma’ruf, M., & Hartini, S. (2019). Paradigma Teori Atom Lintas Waktu. Jurnal Filsafat Indonesia, 2(1), 42. https://doi.org/10.23887/jfi.v2i1.17551
Sutrisna, I., Nasrun, A., Bahri, M., & Toaha, S. (2019). Transformasi Fourier Fraksional dari Fungsi Gaussian. Jurnal Matematika, Statistika Dan Komputasi, 16(1), 19. https://doi.org/10.20956/jmsk.v16i1.5939
Uhl, D., Wituschek, A., Michiels, R., Trinter, F., Jahnke, T., Allaria, E., Callegari, C., Danailov, M., Di Fraia, M., Plekan, O., Bangert, U., Dulitz, K., Landmesser, F., Michelbach, M., Simoncig, A., Manfredda, M., Spampinati, S., Penco, G., Squibb, R. J., … Bruder, L. (2022). Extreme Ultraviolet Wave Packet Interferometry of the Autoionizing HeNe Dimer. The Journal of Physical Chemistry Letters, 13(36), 8470–8476. https://doi.org/10.1021/acs.jpclett.2c01619
Zhu, H., Duan, X., Fan, S., Wu, H., Lin, X., Ning, Y., & Wang, L. (2020). Scalable structure of coherent polarization beam combining based on tapered diode laser amplifiers. Optics & Laser Technology, 132(106470), 106470. https://doi.org/10.1016/j.optlastec.2020.106470
Author Biography
Dewi Wulandari, Universitas Negeri Medan
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