function [psi] = propagate(this,psi,Params,Transf,VDk,V,njob,t_idx,Observ)
    set(0,'defaulttextInterpreter','latex')
    set(groot, 'defaultAxesTickLabelInterpreter','latex'); set(groot, 'defaultLegendInterpreter','latex');
    
    dt=-1j*abs(this.TimeStep);
    
    KEop= 0.5*(Transf.KX.^2+Transf.KY.^2+Transf.KZ.^2);
    Observ.residual = 1; Observ.res = 1; 
    
    muchem = this.Calculator.ChemicalPotential(psi,Params,Transf,VDk,V);
    AdaptIdx = 0;
    
    while t_idx < Params.cut_off
        %kin
        psi = fftn(psi);
        psi = psi.*exp(-0.5*1i*dt*KEop);
        psi = ifftn(psi);
        
        %DDI
        frho = fftn(abs(psi).^2);
        Phi = real(ifftn(frho.*VDk));
        
        %Real-space
        psi = psi.*exp(-1i*dt*(V + Params.gs*abs(psi).^2 + Params.gdd*Phi + Params.gammaQF*abs(psi).^3 - muchem));
    
        %kin
        psi = fftn(psi);
        psi = psi.*exp(-0.5*1i*dt*KEop);
        psi = ifftn(psi);
       
        %Renorm
        Norm = trapz(abs(psi(:)).^2)*Transf.dx*Transf.dy*Transf.dz;
        psi = sqrt(Params.N)*psi/sqrt(Norm);
    
        muchem = this.Calculator.ChemicalPotential(psi,Params,Transf,VDk,V);
    
        if mod(t_idx,1000) == 0        
    
            %Change in Energy
            E = this.Calculator.TotalEnergy(psi,Params,Transf,VDk,V);
            E = E/Norm;
            Observ.EVec = [Observ.EVec E];
    
            %Chemical potential
            Observ.mucVec = [Observ.mucVec muchem];
    
            %Normalized residuals
            res = this.Calculator.NormalizedResiduals(psi,Params,Transf,VDk,V,muchem);
            Observ.residual = [Observ.residual res];
            
            Observ.res_idx = Observ.res_idx + 1;
    
            save(sprintf('./Data/Run_%03i/psi_gs.mat',njob),'psi','muchem','Observ','t_idx','Transf','Params','VDk','V');
            
            %Adaptive time step -- Careful, this can quickly get out of control
            relres = abs(Observ.residual(Observ.res_idx)-Observ.residual(Observ.res_idx-1))/Observ.residual(Observ.res_idx);
            if relres <1e-5
                if AdaptIdx > 4 && abs(dt) > Params.mindt
                    dt = dt / 2;
                    fprintf('Time step changed to '); disp(dt);
                    AdaptIdx = 0;
                elseif AdaptIdx > 4 && abs(dt) < Params.mindt
                    break
                else
                    AdaptIdx = AdaptIdx + 1;
                end
            else
                AdaptIdx = 0;
            end
        end
        if any(isnan(psi(:)))
            disp('NaNs encountered!')
            break
        end
        t_idx=t_idx+1;
    end
    
    %Change in Energy
    E = this.Calculator.TotalEnergy(psi,Params,Transf,VDk,V);
    E = E/Norm;
    Observ.EVec = [Observ.EVec E];
    
    % Phase coherence
    [PhaseC] = this.Calculator.PhaseCoherence(psi,Transf,Params);
    Observ.PCVec = [Observ.PCVec PhaseC];
    
    Observ.res_idx = Observ.res_idx + 1;
    save(sprintf('./Data/Run_%03i/psi_gs.mat',njob),'psi','muchem','Observ','t_idx','Transf','Params','VDk','V');
end