Ground state properties of tonks-girardeau gas in harmonic oscillator potential with multiple 𝛿- perturbations - Cosme, Jayson G. (National Institute of Physics, College of Science, University of the Philippines Diliman, 2013)
The ground state properties of a Tonks-Girardeau gas experiencing harmonic oscillator confinement and multiple 𝛿 -perturbations are studied. Specifically, the ground-state energy, the single-particle density profile, and the pair-correlation function are obtained for different systems with varying number of bosons and 𝛿 - barrier spacing and strength. Using the Fermi-Bose mapping theorem the system is mappled into that of noninteracting spinless fermions.The eigenfunction of the single fermionic counterpart is calculated by rewriting the Time-Independent Schrodinger equation to a Weber differential equation. Then the procedure for constructing the single particle eigenstates numerically is discussed in detail. As expected, the 𝛿 - perturbations, in general, increase the total ground state energy of the system. From the single-particle density and pair-correlation function, it was found out the presence of 𝛿 -perturbations has a seemingly "localization" effect on the bosons.