Show that the symmetric and anti symmetric combinations of $\mathbf{(}\mathbf{8}\mathbf{-}\mathbf{19}\mathbf{)}$and$\mathbf{(}\mathbf{8}\mathbf{-}\mathbf{20}\mathbf{)}$are solutions of the two. Particle Schrödinger equation$\mathbf{(}\mathbf{8}\mathbf{-}\mathbf{13}\mathbf{)}$of the same energy as${\mathbf{\psi }}_{\mathbf{n}}\mathbf{\left(}{\mathbf{x}}_{\mathbf{1}}\mathbf{\right)}{\mathbf{\psi }}_{\mathbf{m}}\mathbf{\left(}{\mathbf{x}}_{\mathbf{2}}\mathbf{\right)}$, the unsymmetrized product$\mathbf{(}\mathbf{8}\mathbf{-}\mathbf{17}\mathbf{)}$.

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