In the present work we determine the speed of sound in a Bose-Einstein condensate confined by an isotropic harmonic oscillator trap. The deduction of this physical parameter is done resorting to the $N$ -body Hamiltonian operator. The single-particle eigenfunctions that have been employed in this formalism are those stemming from the corresponding harmonic oscillator potential, and an expression for the dependence of this speed on the temperature is also deduced. These functions are used in the calculation of the scaterring length, etc. The situation for a Bose-Einstein condensate of sodium is evaluated and the corresponding speed of sound is obtained and compared against the known experimental outcomes. The possibility that the solution, to the existing discrepancy between experiment and theoretical predictions, could be given by the Zaremba-Nikuni-Griffin formalism is also explored.In the present work we determine the speed of sound in a Bose-Einstein condensate confined by an isotropic harmonic oscillator trap. The deduction of this physical parameter is done resorting to the $N$-body Hamiltonian operator. The single-particle eigenfunctions that have been employed in this formalism are those stemming from the corresponding harmonic oscillator potential, and an expression for the dependence of this speed on the temperature is also deduced. These functions are used in the calculation of the scaterring length, etc. The situation for a Bose-Einstein condensate of sodium is evaluated and the corresponding speed of sound is obtained and compared against the known experimental outcomes. The possibility that the solution, to the existing discrepancy between experiment and theoretical predictions, could be given by the Zaremba-Nikuni-Griffin formalism is also explored.

arXiv:1205.4774May 21, 20121 citation

The Quantum Harmonic Oscillator

Michele Cini

UNITEXT for physicsJan 1, 20240 citations

In the present work we determine the speed of sound in a Bose-Einstein condensate confined by an isotropic harmonic oscillator trap. The deduction of this physical parameter is done resorting to the

N

-body Hamiltonian operator. The single-particle eigenfunctions that have been employed in this formalism are those stemming from the corresponding harmonic oscillator potential, and an expression for the dependence of this speed on the temperature is also deduced. These functions are used in the calculation of the scaterring length, etc. The situation for a Bose-Einstein condensate of sodium is evaluated and the corresponding speed of sound is obtained and compared against the known experimental outcomes. The possibility that the solution, to the existing discrepancy between experiment and theoretical predictions, could be given by the Zaremba-Nikuni-Griffin formalism is also explored.