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 square-well potential
  • derive the time-independent 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