Uncertainty of Helium Ion Momentum (𝑯𝒆+) by Using the Heisenberg Uncertainty Approach on Quantum Numbers 𝒏 ≤ 𝟑

Abstract

This study aims to find the uncertainty value of Helium Ion Momentum (𝐻𝑒+) by using the Heisenberg Uncertainty Approach to Quantum Numbers 𝑛 ≤ 3. This type of research uses non-experimental research. The research was conducted by developing previously existing theories. This research is to calculate the expectation value of the position to find out how often electrons can appear, and determine the uncertainty of the momentum of Helium Ion (𝐻𝑒+) by using the Heisenberg uncertainty approach at number 𝑛 ≤ 3. Based on the results and discussion, it can be concluded that the uncertainty of helium ion momentum (𝐻𝑒+) by using the Heisenberg uncertainty approach to quantum numbers 𝑛 ≤ 3. The uncertainty of helium ion momentum is influenced by the main quantum number (n) and the azimuthal quantum number (l). By entering the values of n and l, the results can be obtained at quantum numbers 𝑛 = 1 with 𝑙 = 0 obtained ∆𝑃𝑟 = 2,977504663 × 10−24. At the quantum number 𝑛 = 2 with 𝑙 = 0 obtained ∆𝑃𝑟 = 8,06312759 × 10−24 and 𝑙 = 1 obtained ∆𝑃𝑟 = 2,03048 × 10−23. At the quantum number 𝑛 = 3 with 𝑙 = 0 obtained ∆𝑃𝑟 = 1,50366086 × 10−23, and 𝑙 = 1 obtained ∆𝑃𝑟 = 3,481407588 × 10−23 and 𝑙 = 2 obtained ∆𝑃𝑟 = 4,47363642 × 10−22. Based on these results, it can be concluded that the uncertainty value of momentum is getting bigger as the two values of n and l increase. This is also proven by using simulation and the results of momentum uncertainty are not much different and only a difference of a few decimal places.