Question: The wave function 0 (x) = Ae -x2/2L 2 represents the ground-state energy of a harmonic oscillator. (a) Show that 1 (x) =

The wave function Ψ0(x) = Ae-x2/2L2 represents the ground-state energy of a harmonic oscillator. 

(a) Show that Ψ1(x) = LdΨ0(x)/dx is also a solution of Schrödinger’s equation.

(b) What is the energy of this new state? 

(c) From a look at the nodes of this wave function, how would you classify this excited state?

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