Objectives
Following your study of this chapter, you should be able to:
 compare the classical wave equation with the Schrödinger wave equation
 given a wave equation, determine whether it satisfies a form of the Schrödinger equation
 state the four boundary conditions for a valid wave function
 derive the time independent Schrödinger wave equation from the time dependent form
 understand what is meant by "operator"
 calculate the expectation values of momentum and energy using the appropriate operators
 calculate expectation values for all the potentials discussed in the chapter
 invoke boundary conditions of an infinite square well potential to derive equations for the wave function and energy
 follow the discussion in the text for applying boundary conditions of a finite squarewell potential
 derive the timeindependent Schrödinger wave equation in three dimensions
 find the wave functions and energies of a free particle in a box
 follow the discussion in the text of the derivation of the simple harmonic oscillator potential
 graph the potential and wave function for a SHO estimate the zeroth point energy of a SHO allowed by the uncertainty princple
 know the wave function solutions and energy levels of a SHO
 apply boundary conditions to regions of potential barriers (>Vo and
 calculate the probability of reflection and transmission of particles incident on a potential barrier
 explain tunneling and find transmission probabilities of particles
 cite experimental evidence of tunneling
