Abstract:We examine the problem of two particles confined in an isotropic harmonic trap, which interact via a finite-ranged Gaussian-shaped potential in two spatial dimensions. We derive an approximative transcendental equation and solved it using exact diagonalization to study the resulting energy spectrum as a function of the inter-particle interaction strength, relative angular momenta and analyse the role of Hilbert space. Both the attractive and repulsive systems are analysed. We study the impact of the potential'… Show more
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