ИСПОЛЬЗОВАНИЕ ЧИСЛЕННЫХ МЕТОДОВ ВЫЧИСЛЕНИЯ НА ПРАКТИЧЕСКИХ ЗАНЯТИЯХ КВАНТОВОЙ МЕХАНИКИ
Article Sidebar
Main Article Content
Abstract:
В статье рассматривается использование численных методов вычисления в процессе проведения практических занятий по квантовой механике. Показано, что применение компьютерного моделирования и современных вычислительных инструментов позволяет преодолеть ограничения аналитических методов, которые часто не позволяют исследовать сложные физические системы с произвольными потенциалами. Особое внимание уделяется применению метода конечных разностей, схемы Кранка–Николсона и специализированных программных библиотек для численного решения уравнения Шрёдингера. Подчеркивается, что интеграция вычислительных технологий в образовательный процесс способствует более глубокому пониманию квантовых явлений, таких как туннелирование, интерференция и динамика волновых пакетов.
Article Details
How to Cite:
References:
Srnec MN, Upadhyay S, Madura JD. A Python Program for Solving Schrödinger’s Equation in Undergraduate Physical Chemistry. Journal of Chemical Education [Internet]. 2017 Apr 17 [cited 2025 Nov];94(6):813. Available from: https://doi.org/10.1021/acs.jchemed.7b00003
Jelic V, Marsiglio F. The double-well potential in quantum mechanics: a simple, numerically exact formulation. European Journal of Physics [Internet]. 2012 Sep 14 [cited 2025 Oct];33(6):1651. Available from: https://doi.org/10.1088/0143-0807/33/6/1651
Ahmed SZ, Jensen JHM, Weidner CA, Sørensen JJ, Mudrich M, Sherson J. Quantum composer: A programmable quantum visualization and simulation tool for education and research. American Journal of Physics [Internet]. 2021 Feb 19 [cited 2025 Oct];89(3):307. Available from: https://doi.org/10.1119/10.0003396
Jugdutt BA, Marsiglio F. Solving for three-dimensional central potentials using numerical matrix methods. American Journal of Physics [Internet]. 2013 Apr 16 [cited 2025 Sep];81(5):343. Available from: https://doi.org/10.1119/1.4793594
Schroeder DV. The variational-relaxation algorithm for finding quantum bound states. American Journal of Physics [Internet]. 2017 Aug 18 [cited 2025 Sep];85(9):698. Available from: https://doi.org/10.1119/1.4997165
Zhu G, Hu J, Du C. Assisting Tibetan Students in Learning Quantum Mechanics via Mathematica. arXiv (Cornell University) [Internet]. 2024 Jun 26 [cited 2025 Sep]; Available from: http://arxiv.org/abs/2406.18810
McKagan SB, Perkins KK, Wieman C. Deeper look at student learning of quantum mechanics: The case of tunneling. Physical Review Special Topics - Physics Education Research [Internet]. 2008 Oct 8 [cited 2025 Nov];4(2). Available from: https://doi.org/10.1103/physrevstper.4.020103
Ahmed SZ, Weidner CA, Jensen JHM, Sherson J, Lewandowski HJ. Student use of a quantum simulation and visualization tool. European Journal of Physics [Internet]. 2022 Sep 21 [cited 2025 Oct];43(6):65703. Available from: https://doi.org/10.1088/1361-6404/ac93c7
Ahmed SZ, Weidner CA, Jensen JHM, Sherson J, Lewandowski HJ. Student engagement and learning with Quantum Composer. arXiv (Cornell University) [Internet]. 2021 Apr 27 [cited 2025 Oct]; Available from: http://arxiv.org/abs/2104.13260
Proceedings of the ХIХ International Scientific and Practical Conference. 2022 Jun 9 [cited 2025 Jul]; Available from: https://doi.org/10.46299/isg.2022.1.19
Баранов АВ, Volochovich EN, Medvedeva KA, Stepin DV. EDUCATIONAL COMPUTER SIMULATION EXPERIMENT «REAL-TIME SINGLE-MOLECULE IMAGING OF QUANTUM INTERFERENCE». Open Education [Internet]. 2015 Jan 1 [cited 2025 Oct];110. Available from: https://doi.org/10.21686/1818-4243-2015-3(110-110-114
Kabir A. Numerical Simulation of the Time-Dependent Schrodinger Equation Using the Crank-Nicolson Method. arXiv (Cornell University) [Internet]. 2024 Oct 13 [cited 2025 Sep]; Available from: http://arxiv.org/abs/2410.10060
Fernández FM. Variational approach to the Schrödinger equation with a delta-function potential. European Journal of Physics [Internet]. 2021 Dec 1 [cited 2025 Sep];43(2):25401. Available from: https://doi.org/10.1088/1361-6404/ac3f27
Valle JC del. Solving the one-dimensional time-independent Schrödinger equation with high accuracy: The LagrangeMesh Mathematica® package. International Journal of Modern Physics C [Internet]. 2023 May 26 [cited 2025 Nov];35(1). Available from: https://doi.org/10.1142/s0129183124500116
Passante G, Kohnle A. Enhancing student visual understanding of the time evolution of quantum systems. Physical Review Physics Education Research [Internet]. 2019 Feb 13 [cited 2025 Nov];15(1). Available from: https://doi.org/10.1103/physrevphyseducres.15.010110
Stippell E, Akimov AV, Prezhdo OV. PySyComp: A Symbolic Python Library for the Undergraduate Quantum Chemistry Course. Journal of Chemical Education [Internet]. 2023 Sep 19 [cited 2025 Nov];100(10):4077. Available from: https://doi.org/10.1021/acs.jchemed.2c00974
McKagan SB, Perkins KK, Dubson M, Malley C, Reid S, LeMaster R, et al. Developing and researching PhET simulations for teaching quantum mechanics. American Journal of Physics [Internet]. 2008 Mar 13 [cited 2025 Sep];76(4):406. Available from: https://doi.org/10.1119/1.2885199
Cruzeiro VWD, Gao X, Kleiman VD. Implementing New Educational Platforms in the Classroom: An Interactive Approach to the Particle in a Box Problem. Journal of Chemical Education [Internet]. 2019 Jul 11 [cited 2025 Nov];96(8):1663. Available from: https://doi.org/10.1021/acs.jchemed.9b00195
Lancaster JL, Allen DB. Simulating spin dynamics with quantum computers. American Journal of Physics [Internet]. 2024 Dec 23 [cited 2025 Sep];93(1):98. Available from: https://doi.org/10.1119/5.0112717
Solorio CD, Gire E, Roundy D. Student understandings of discrete and continuous in quantum mechanics: A thematic analysis. Physical Review Physics Education Research [Internet]. 2025 Nov 4 [cited 2026 Feb];21(2). Available from: https://doi.org/10.1103/4q6g-yq88
Gharibnejad H, Schneider BI, Leadingham M, Schmale HJ. Comparison of Numerical Approaches to the Time-Dependent Schr"odingern Solutions in One Dimension. arXiv (Cornell University) [Internet]. 2018 Sep 24 [cited 2025 Oct]; Available from: http://arxiv.org/abs/1809.09164
Weidner CA, Ahmed SZ, Jensen JHM, Sherson J, Lewandowski HJ. Investigating student use of a flexible tool for simulating and visualizing quantum mechanics. In: 2017 Physics Education Research Conference Proceedings [Internet]. 2020 [cited 2025 Oct]. Available from: https://doi.org/10.1119/perc.2020.pr.weidner
Guttieres LAJ, Petrović MD, Freericks JK. Computational projects with the Landau-Zener problem in the quantum mechanics classroom. arXiv (Cornell University) [Internet]. 2023 Jun 21 [cited 2025 Oct]; Available from: http://arxiv.org/abs/2306.11633
Galante L. Blowing in a drinking straw: introducing quantum physics. arXiv (Cornell University) [Internet]. 2025 Jun 13 [cited 2025 Oct]; Available from: http://arxiv.org/abs/2506.11524
Sánchez LH, Garay IAB, Rosas AF, Prieto IR, Soto‐Eguibar F, Moya-Cessa HM. Numerical solution of the Lindblad master equation using the Runge-Kutta method implemented in Python. arXiv (Cornell University) [Internet]. 2025 Jun 24 [cited 2025 Oct]; Available from: http://arxiv.org/abs/2506.19238
Haraldsrud A, Odden TOB. Using feedback loops from computational simulations as resources for sensemaking: a case study from physical chemistry. Chemistry Education Research and Practice [Internet]. 2024 Jan 1 [cited 2025 Nov];25(3):760. Available from: https://doi.org/10.1039/d4rp00017j
Kohnle A, Baily C, Hooley C, Torrance B. Optimization of Simulations and Activities for a New Introductory Quantum Mechanics Curriculum. In: 2017 Physics Education Research Conference Proceedings [Internet]. 2014 [cited 2025 Sep]. Available from: https://doi.org/10.1119/perc.2013.pr.040