Free-particle
A. Suppose that the wavefunction for a free-particle is given by the wavefunction
Find the value of A that normalizes Ψ (x).
B. The Hamiltonian operator for a free particle is just the kinetic energy operator
Is Ψ(x) an eigenfunction of the free-particle Hamiltonian?
C. Can the energy for a quantum mechanical free particle ever be "well-defined"? Why or why not?
D. Compute the expectation (average) value of < H >, < p >, and < x > for the Ψ(x) given.
E. What is the uncertainty in total energy as a function of the parameter, σ_{x}?