SIMULASI PERMASALAHAN BENDA JATUH DALAM KALKULUS KUANTUM

Authors

  • Kistosil Fahim Institut Teknologi Sepuluh Nopember
  • DZAKY MUHAMMAD
  • MAHMUD YUNUS
  • I GUSTI NGURAH RAI USADHA
  • SUNARSINI SUNARSINI
  • SADJIDON SADJIDON

DOI:

https://doi.org/10.25077/jmua.13.1.14-25.2024

Keywords:

$q$-Calculus, exact solution, series-$q$, Falling body problem, Differential equation-$q$, SImulation

Abstract

Kalkulus kuantum yang selanjutnya disebut sebagai kalkulus-$q$ merupakan cabang baru dari ilmu matematika dimana konsep derivatif dari sebua fungsi real dapat dihitung tanpa menggunakan limit. Pada paper ini membahas sebuah permasalahan benda jatuh dalam media penahan dengan sudut pandang kalkulus-$q$. Persamaan diferensial-$q$ yang mendeskripsikan kecepatan vertikal telah didapatkan. sehingga berdasarkan hal ini persamaan eksak untuk kecepatan vertikal dan jarak vertikal telah tersedia. Penyelesaian yang didapatkan diekspresikan ke dalam suku fungsi eksponensial-$q$ yang mana fungsi dasar dari kalkulus-$q$. Dimensionalitas dari formula kecepatan dan jarak juga dianalisis. Sebagai tambahan penyelesaian eksak yang ada akan menyerupai penyelesaian versi klasiknya dalam mekanika Newton ketika parameter kuantum q mendekati satu. Selain itu untuk melihat perilaku dari penyelesaian yang didapatkan terdapat simulasi dengan memperhatikan dua parameter yang berubah, yaitu jumlah suku pada fungsi eksponensial-{$q$} dan parameter kuantum $q$.

References

Alanazi AM, Ebaid A, Alhawiti WM and Muhiuddin G (2020) The Falling Body Problem in Quantum Calculus. Front. Phys. 8:43. doi: 10.3389/fphy.2020.00043

Kac, V dan Cheung, P. 2002. Quantum Calculus. Edisi ke-1. Universitext. Amerika Utara.

Subiono. 2023. Kalkulus Kuantum. Versi 1.0.0. Departemen Matematika ITS. ITS News.

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Published

31-01-2024

Issue

Vol. 13 No. 1 (2024)

Section

Articles

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