A particle is subject to a potential energy that has an essentially infinitely high wall a...

A particle is subject to a potential energy that has an essentially infinitely high wall al the origin, like the infinite well, but for positive values of x is of the form

U(x)=-b/x, where b is a constant, (a) Sketch this potential energy, (b) How much energy could a classical particle have and still be bound by such a potential energy? (c) Add to your sketch a plot of £ for a bound particle and indicate the outer classical turning point (the inner being the origin), (d) Assuming that a quantum-mechanical description is in order, sketch a plausible ground-state wave function, making sure that your function's second derivative is of the proper sign when U(x) is less than E and when it is greater.