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Modeling the quantum world requires a view of waves and those waves in the presence of a potential.  Like the electronic potential particles bound to an atom experience a similar force.  To begin to understand wavefunctions in the presence of this potential we begin with basic potentials then work our way up.   

    Wavefunctions that enter a region of different potential can be solved with the continuity conditions.  These are that the wavefunction and its first derivative must be equal across the boundary.  By applying these simple continuity conditions a lot can be learned about the nature of waves.  Go through this Maple worksheet and answer these questions. 

        1.  Describe what happens to the waveform when entering a region of higher potential.  What happens when the potential is greater then the energy of the wave.  

        2.  What is the condition for resonance in a well?  How about in across a barrier when the energy is greater then the barrier.  

        3.  How can you justify quantum tunneling.  

        4.  In the classical limit the energy of the wave is magnitudes greater then the potential.  In this limit how does the wavefunction change?   

        5.  For the double potential step describe the wave in terms of the right and left wave components for all three regions.  

        6.  When there is only a wave traveling to the right, i.e. after the last potential change, what can be said about the probability?   

        7.  Since the probability is the complex conjugate of the wavefunction times the wavefunction what can be said about the real and imaginary parts in a region of constant probability?   

Rutherford Scattering

     Early physicist attempting to understand the quantum world learned a great deal through scattering experiments.  Like it sounds particles are incident on an atom and the scattering of these particles was observed.  This allowed an ability to describe the potential that was scattering those particles.  View this applet.

        1.  How could this experiment tell you information about the potential created by the nucleus?  

Bohr Model of an Atom

     In 1913 Niels Bohr suggested a planetary model for the atom.  Through quantization of angular momentum the discrete nature of allowed energy levels began to rise.  View this applet of this model and answer the questions. 

        1.  What happens when the incident photons energy is increased?

        2.  Does the excited electron have to go directly back down to the ground state or can it take multiple paths?  What is the affect of those multiple paths?