On the Two Body Interaction Energy In Common Harmonic Oscillator Potential

Patrick Shea, Brandon P. van Zyl, Rajat K. Bhaduri

We consider two bosonic atoms interacting with a short-range potential and trapped in a spherically symmetric harmonic oscillator. The problem is exactly solvable and is relevant for the study of ultra-cold atoms. We show that the energy spectrum is universal, irrespective of the shape of the interaction potential, provided its range is much smaller than the oscillator length.

Twisha Choudhary

This study presents a comprehensive analysis of the two-body central-interaction problem in quantum mechanics. We investigate the Schrödinger equation for two particles interacting through a central potential, and derive the radial and angular parts of the wave function. The energy eigenvalues and Eigen functions are obtained for various central potentials, including the Coulomb, harmonic oscillator, and square well potentials.

Carlo Jacoboni

J R Armstrong, Artem G. Volosniev, D V Fedorov +2 more

We describe a procedure to solve an up to problem where the particles are separated topologically in N groups with at most two particles in each. Arbitrary interactions are allowed between the (two) particles within one group. All other interactions are approximated by harmonic oscillator potentials. The problem is first reduced to an analytically solvable N -body problem and N independent two-body problems. We calculate analytically spectra, wave functions, and normal modes for both the inverse square and delta-function two-body interactions. In particular, we calculate separation energies between two strings of particles. We find that the string separation energy increases with N and interaction strength.