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

Urease is an enzyme that functions as a catalyst in the hydrolysis of urea into ammonia and carbon dioxide. The industrial sector has made extensive use of urease. To date, enzymes are used in free form, deemed less effective. Therefore, enzymes are used in immobilized form because they can be utilized repeatedly. This research aimed to isolate urease from kidney bean (Phaseolus vulgaris L.) seed and immobilize it using a Ca-alginate support matrix and a trapping technique. Eight days were devoted to germinating kidney bean seeds to begin the investigation. Isolation of crude urease extract from kidney beans was carried out using phosphate buffer pH 7. It was then immobilized with Ca-alginate at different concentrations of Na-alginate and contact times The crude free and immobilized urease extract was further characterized including pH, temperature and stability of repeated use. The urease activity was determined using the Nessler method using a spectrophotometer. The results demonstrated that urease immobilization from kidney bean seeds with a Ca-alginate matrix was most effective at a concentration of 5% Na-alginate and a contact period of 60 minutes, yielding a value of 5.92 U/mL. The optimal pH of free and immobilized urease was 7 and 8, respectively, and temperatures of 35 and 40 °C, respectively. The immobilization of urease from kidney bean seeds using a Ca-alginate support matrix increased the stability of recurrent use by fivefold, while the relative urease activity remained at 52%.