function [psi] = propagateWavefunction(this,psi,Params,Transf,VDk,V,t_idx,Observ)
    
    switch this.SimulationMode
	    case 'ImaginaryTimeEvolution'
            
            dt              = -1j*abs(this.TimeStepSize); % Imaginary Time
            
            KEop            = 0.5*(Transf.KX.^2+Transf.KY.^2+Transf.KZ.^2);
            Observ.residual = 1; 
            Observ.res      = 1; 
            
            muchem          = this.Calculator.calculateChemicalPotential(psi,Params,Transf,VDk,V);
            
            if this.PlotLive
                Plotter.plotLive(psi,Params,Transf,Observ)
                drawnow
            end
            
            AdaptIdx        = 0;
            
            while t_idx < Params.sim_time_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.gammaQF*abs(psi).^3 + Params.gdd*Phi - muchem));
            
                % kin
                psi    = fftn(psi);
                psi    = psi.*exp(-0.5*1i*dt*KEop);
                psi    = ifftn(psi);
               
                % Renorm
                Norm   = sum(abs(psi(:)).^2)*Transf.dx*Transf.dy*Transf.dz;
                psi    = sqrt(Params.N)*psi/sqrt(Norm);
            
                muchem = this.Calculator.calculateChemicalPotential(psi,Params,Transf,VDk,V);
                
                if mod(t_idx,1000) == 0        
            
                    % Change in Energy
                    E               = this.Calculator.calculateTotalEnergy(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.calculateNormalizedResiduals(psi,Params,Transf,VDk,V,muchem);
                    Observ.residual = [Observ.residual res];
                    Observ.res_idx  = Observ.res_idx + 1;
                    
                    if this.PlotLive
                        Plotter.plotLive(psi,Params,Transf,Observ)
                        drawnow
                    end

                    save(sprintf(strcat(this.SaveDirectory, '/Run_%03i/psi_gs.mat'),Params.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.calculateTotalEnergy(psi,Params,Transf,VDk,V);
            E              = E/Norm;
            Observ.EVec    = [Observ.EVec E];
            
            Observ.res_idx = Observ.res_idx + 1;

            disp('Run completed!');
            disp('Saving data...');
            save(sprintf(strcat(this.SaveDirectory, '/Run_%03i/psi_gs.mat'),Params.njob),'psi','muchem','Observ','t_idx','Transf','Params','VDk','V');
            disp('Save complete!');
        
        case 'RealTimeEvolution'

            dt = abs(this.TimeStepSize);
        
            KEop= 0.5*(Transf.KX.^2+Transf.KY.^2+Transf.KZ.^2);
            
            muchem = this.Calculator.calculateChemicalPotential(psi,Params,Transf,VDk,V);
            
            while t_idx < Params.sim_time_cut_off

                % Parameters at time t
                
                %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.gammaQF*abs(psi).^3 + Params.gdd*Phi - muchem));
            
                %kin
                psi = fftn(psi);
                psi = psi.*exp(-0.5*1i*dt*KEop);
                psi = ifftn(psi);
                
                muchem = this.Calculator.calculateChemicalPotential(psi,Params,Transf,VDk,V);
            
                if mod(t_idx,1000)==0        
                    %Change in Normalization
                    Norm = sum(abs(psi(:)).^2)*Transf.dx*Transf.dy*Transf.dz; % normalisation
                    Observ.NormVec = [Observ.NormVec Norm];
            
                    %Change in Energy
                    E = this.Calculator.calculateTotalEnergy(psi,Params,Transf,VDk,V);
                    E = E/Norm;
                    Observ.EVec = [Observ.EVec E];
            
                    Observ.tVecPlot = [Observ.tVecPlot tVal];
                    Observ.res_idx = Observ.res_idx + 1;
                    
                    save(sprintf('./Data/Run_%03i/TimeEvolution/psi_%i.mat',Params.njob,Observ.res_idx),'psi','muchem','Observ','t_idx');        
                end
                if any(isnan(psi(:)))
                    disp('NaNs encountered!')
                    break
                end
                t_idx=t_idx+1;
            end
            
            %Change in Normalization
            Norm = sum(abs(psi(:)).^2)*Transf.dx*Transf.dy*Transf.dz; % normalisation
            Observ.NormVec = [Observ.NormVec Norm];
            
            %Change in Energy
            E = this.Calculator.calculateTotalEnergy(psi,Params,Transf,VDk,V);
            E = E/Norm;
            Observ.EVec = [Observ.EVec E];
            
            % Phase coherence
            [PhaseC] = this.Calculator.calculatePhaseCoherence(psi,Transf);
            Observ.PCVec = [Observ.PCVec PhaseC];
            
            Observ.tVecPlot = [Observ.tVecPlot tVal];
            Observ.res_idx = Observ.res_idx + 1;
            
            disp('Run completed!');
            disp('Saving data...');
            save(sprintf('./Data/Run_%03i/TimeEvolution/psi_%i.mat',Params.njob,Observ.res_idx),'psi','muchem','Observ','t_idx');
            disp('Save complete!');
        
        otherwise
	        disp('Choose a valid DDI cutoff type!')
            return
    end
end