Approximate Solution to the Schrödinger Equation of Exotic Doubly Muonic Helium-like Systems Using Hydrogenic-based Matrix Mechanics

• DOI: 10.20884/1.jm.2024.19.1.11224
• Publication Date: 2024-04-01T08:46:47Z
• Authors: Redi Kristian Pingak; Johanes Eliaser J...; Bernandus Bernandus; Albert Zicko Joha...; Ely Setiawan
• Keywords: Exotic atom; Matrix (chemical analysis)

The approximate solution to the Schrödinger equation of exotic doubly muonic helium-like systems has been obtained using a simple matrix method based on hydrogenic s-states. Each system considered consists positively charged nucleus surrounded by 2 negatively muons XZ+μ-μ- (2 Z 36). present work aims obtain ground-state energies and decompose in terms basis states used. Here, wave function was expressed as linear combination 15 eigenfunctions, each written product two elements Hamiltonian were calculated finally, energy eigenvalue numerically solved with their corresponding eigenvectors. From results, all agreement others from literature, percentage differences between 0.03% 2.05%. analysis probability amplitudes eigenvectors showed that 1s1s state made largest contribution ground systems, approaching 90.99%, 96.98% 98.54% for He2+μ-μ- , Li3+μ-μ- Be4+μ-μ- respectively.
 
 Keywords: Doubly energy, states, mechanics,