g[x_,t_,k_]=1/Sqrt[4*Pi*k*t]Exp[-x^2/(4 k t)]

g[0,1,1]

g[0.,1,1]

N[1/2/Sqrt[Pi]]

Plot[g[x,0.0001,1],{x,-1,1},PlotRange->All]

Animate[Plot[7g[x+2,t,1]+3g[x-5,t,1],{x,-5,10},PlotRange->{0,10}],{t,0.001,3}]