Consider the one-dimensional time-independent Schrödinger equationfor some arbitrary potential V(x). Prove that if a solution p(x) has theproperty that (x) → 0 as r → ±00, then the solution must be nondegen-erate and therefore real, apart from a possible overall phase factor.Hint: Show that the contrary assumption leads to a contradiction.

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Consider the one-dimensional time-independent Schrödinger equation for some arbitrary potential V(x). Prove that if a solution Þ(x) has the property that (x) → 0 as r t00, then the solution must be nondegen- erate and therefore real, apart from a possible overall phase factor. Hint: Show that the contrary assumption leads to a contradiction.

Consider the one-dimensional time-independent Schrödinger equation for some arbitrary potential V(x). Prove that if a solution Þ(x) has the property that (x) → 0 as r t00, then the solution must be nondegen- erate and therefore real, apart from a possible overall phase factor. Hint: Show that the contrary assumption leads to a contradiction.

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