Abstract

• Quantum system with 3D harmonic oscillator well is one of the few problems in quantum mechanics that can be solved analytically. In this work, variational principle is applied to calculate eigenvalues and eigenstates of 3D harmonic oscillator system. The trial wave function is chosen as a linear superposition of Gaussian basis function of the form rmie− r2 ? ?2 . To validate the variational results, a numerical approach known as Numerov method is also used to calculate energy values and wave functions. The calculated values are further compared with analytical solutions. The results demonstrate that for a basis size of twelve, the energy values for low-lying states up to N = 15 agree very well with t