diff --git a/Quasi2DBogoliubovSpectrum.m b/Quasi2DBogoliubovSpectrum.m
index 0b27b1b..388ea77 100644
--- a/Quasi2DBogoliubovSpectrum.m
+++ b/Quasi2DBogoliubovSpectrum.m
@@ -68,7 +68,8 @@ xlabel('$k_{\rho}a_{dd}$','fontsize',16,'interpreter','latex')
 ylabel('$\epsilon(k_{\rho})/h$ (Hz)','fontsize',16,'interpreter','latex')
 grid on
 
-%% Bogoliubov excitation spectrum for quasi-2D dipolar gas with QF correction
+%% For different interaction strengths
+
 AtomNumber        = 1E5;                                                                             % Total atom number in the system
 wz                = 2 * pi * 72.4;                                                                   % Trap frequency in the tight confinement direction
 lz                = sqrt(PlanckConstantReduced/(Dy164Mass * wz));                                    % Defining a harmonic oscillator length
@@ -123,7 +124,8 @@ ylabel('$\epsilon(k_{\rho})/h$ (Hz)','fontsize',16,'interpreter','latex')
 grid on
 legend('location', 'northwest','fontsize',16, 'Interpreter','latex')
 
-%% Bogoliubov excitation spectrum for quasi-2D dipolar gas with QF correction
+%% For 3 points on the roton instability boundary
+
 wz                = 2 * pi * 72.4;                                                                   % Trap frequency in the tight confinement direction
 lz                = sqrt(PlanckConstantReduced/(Dy164Mass * wz));                                    % Defining a harmonic oscillator length
 alpha             = 0;                                                                               % Polar angle of dipole moment
@@ -175,6 +177,9 @@ ylabel('$\epsilon(k_{\rho})/h$ (Hz)','fontsize',16,'interpreter','latex')
 grid on
 legend('location', 'northwest','fontsize',16, 'Interpreter','latex')
 
+%% Mean widths of the variational Gaussian ansatz - extremize the total mean field energy per particle wrt to the variational parameter
+
+
 %%
 function [Go,gamma4,Fka,Ukk] = computePotentialInMomentumSpace(k, gs, gdd, MeanWidth, alpha, phi)
    Go                        = sqrt(pi) * (k * MeanWidth/sqrt(2)) .* exp((k * MeanWidth/sqrt(2)).^2) .* erfc((k * MeanWidth/sqrt(2)));