In a certain region of space, a particle is described by the wave function ψ=Cxe−bx where C is a real constants, b =0.5, and m=3.2. By substituting into the Schrodinger equation, find the potential energy (not necessarily constant) in this region and also find the energy of the particle. (Hint: Your solution must give an energy that is a constant everywhere in this region, independent of x.)

In a certain region of space, a particle is described by the wave function ψ=Cxe−bx where C is a real constants, b =0.5, and m=3.2. By substituting into the Schrodinger equation, find the potential energy (not necessarily constant) in this region and also find the energy of the particle. (Hint: Your solution must give an energy that is a constant everywhere in this region, independent of x.)