Mathematics Behind the Heisenberg Uncertainty Principle







Vol. 9 No. 4 (2023): April


Fourier series, Heisenberg uncertainty, Integral transform, Wave packet

Research Articles


How to Cite

Wulandari, D. (2023). Mathematics Behind the Heisenberg Uncertainty Principle. Jurnal Penelitian Pendidikan IPA, 9(4), 2223–2228.


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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.


Amico, M., & Dittel, C. (2020). Simulation of wave-particle duality in multipath interferometers on a quantum computer. Physical Review A, 102(3), 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).

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.

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.

Carosso, A. (2022). Quantization: History and problems. Studies in History and Philosophy of Science, 96, 35–50.

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.

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.

Dolce, D. (2023). Is time a cyclic dimension? Canonical quantization implicit in classical cyclic dynamics. Annals of Physics, 448, 169182.

Firman, H. (2019). Kepastian Dan Ketidakpastian Dalam Sains. Jurnal Filsafat Indonesia, 2(1), 33.

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.

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.

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).

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.

Pebralia, J. (2020). Prinsip Ketidakpastian Heisenberg dalam Tinjauan Kemajuan Pengukuran Kuantum di Abad 21. Journal Online of Physics, 5(2), 43–47.

Ray, A. (2023). Radiation effects and hardening of electronic components and systems: an overview. Indian Journal of Physics.

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.

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.

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.

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).

Sujito, S., Sunardi, S., Ma’ruf, M., & Hartini, S. (2019). Paradigma Teori Atom Lintas Waktu. Jurnal Filsafat Indonesia, 2(1), 42.

Sutrisna, I., Nasrun, A., Bahri, M., & Toaha, S. (2019). Transformasi Fourier Fraksional dari Fungsi Gaussian. Jurnal Matematika, Statistika Dan Komputasi, 16(1), 19.

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.

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.

Author Biography

Dewi Wulandari, Universitas Negeri Medan


Copyright (c) 2023 Dewi Wulandari

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