A fellow student proposes that a possible wave function for a free particle with mass m (one for which the potential-energy function U(x) is zero) is where K is a positive constant(a) Graph this proposed wave function.(b) Show that the proposed wave function satisfies the Schrodinger equation for x (c) Show that the proposed wave functions also satisfies the Schrodinger equation for x > 0 with the same energy as in part (b).(d) Explain why the proposed wave function is nonetheless not an acceptable solution of the Schrodinger equation for a free particle. It is in fact impossible for a free particle (one for which U(x) = 0) to have an energy less thanzero.

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