NIntegrate[Exp[-(x^2)], {x, 0, 1}]

ϵ = 0.8086165;
lasolucion = 
        NDSolve[{ψ''[x] + 
                2 (ϵ - Abs[x]) ψ[x] == 
              0, ψ'[0] == 0, ψ[0] == 
              1}, ψ, {x, -10, 10}];
Plot[Evaluate[ψ[x] /. lasolucion], {x, -8, 8}]

ϵ = 5.8513;
lasolucion = 
        NDSolve[{ψ''[x] + 
                2 (ϵ - Abs[x]) ψ[x] == 
              0, ψ'[0] == 0, ψ[0] == 
              1}, ψ, {x, -20, 20}];
Plot[Evaluate[ψ[x] /. lasolucion], {x, -9, 9}]

ϵ = 3.82571529
lasolucion = 
        NDSolve[{ψ''[x] + 
                2 (ϵ - Abs[x]) ψ[x] == 
              0, ψ'[0] == 0, ψ[0] == 
              1}, ψ, {x, -20, 20}];
Plot[Evaluate[ψ[x] /. lasolucion], {x, -10, 10}]

ϵ = 0.808616;
lasolucion = 
        NDSolve[{ψ''[x] + 
                2 (ϵ - Abs[x]) ψ[x] == 
              0, ψ'[0] == 0, ψ[0] == 
              1}, ψ, {x, -10, 10}];
Plot[Evaluate[ψ[x] /. lasolucion], {x, -8, 8}]