Objectives

• 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