1) Consider the following example of a quantum mechanicalwavefunction for a particle of mass m moving in one dimension,where α and A are constants.
?(?, ?) = ?? − ?(?2 + ?�/?) ,
a) Normalize the wavefunction. Show your work.
b) At what value of x is there equal probability for the particleto be either to the left or to the right of that x? Show your workand explain.
c) For the wavefunction given, what must the potential V (x, t) bein order for Ψ(x, t) to satisfy the Schrodinger equation? Whatclassical system has this kind of potential?
d) Calculate the expectation values of x, x2, p, and p2. Explain inwords what each calculation means (how it is related tomeasurement).
e) Determine ?! and ?\" and check if their product is consistentwith the uncertainty principle.
