Why are the solutions of the time independent Schrodinger equation for free particles not really acceptable states?
How is that problem cured by considering solution of the time dependent Schrodinger equation?
How does one distinguish a wave runnign right from a wave running left among the (non-normalizable) solutions of the free-particle Schrodinger equation?
What is the phase velocity and how does it differ from the group velocity, or particle velocity?
Why there is no such thing as a free particle state with a definite momentum?
What is a wave packet?
What is Fourier transformation? What is the inverse of a Fourier transform?
What is the physical meaning of the group velocity in term of a wave packet?
What is a delta function? /LI>
Why is an attractive potential a requirement of the existence of a bound state?
How does one get the boundary conditions for the delta function potential?
What is the distinction between a scattering state and a bound state?
What is the difference between the spectra of bound states and scattering states?
How many bound states does an attractive delta function potential have?
Using the fact that the delta function has dimension [1/x] use dimensional analysis to give a fast estimate of the dependence of the bound state energy of the delta function potential on its coefficient, alpha, the particle mass, and hbar.
Without solving the delta function potential problem, what would you think how the bound state energy depends on alpha, the coefficient of the delta function?
Scattering states having a definite energy are not normalizable. Still, many results derived using these states carry over to well defined normalizable scattering states. Why is this so?
What are the reflection and transmission coefficents and what conditions do they satisfy? What is the physical interpretation of that condition?
Suppose one has a repulsive delta function potential (delta function with a positive multiplier). Does the system have bound states?
What is the tunnel effect and how does it apply to scattering on a repulsive delta function potential?