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This week will expand on the concept of Quantum waves and the Schrödinger approach to wave solutions.  

    A single wave is easy to visualize as sinusoidal function through space.  Once the concept of superposition of waves is introduced a few more visual concepts are needed.   Specifically the introduction of group and phase velocity.  View this applet and read the explanation. 

        1.  What is the effect of setting the group velocity to a value greater then one?

        2.  What is the effect of setting the group velocity to a value less then one? 

        3.  In your own words what is the difference between the group and phase velocity?

Bound States

    For a particle trapped in a potential the Schrödinger equation only allows discrete solutions.  The first example is a particle trapped in an infinite well.  Like a string attached to two concrete walls only integer and half integer wavelengths are stable.  This applet allows you to look at the wave functions for an infinite well and other non-infinite potentials.  Read how to operate the applet before trying to understand it.  

        1.  For the infinite well what do you notice about the wave function as you increase the energy level.  

        2.  Double click on an energy level with the phasor circles on the bottom.  Now add an additional energy level by single clicking on a different energy level.  What do you notice about the total wave function?  Is it static?   Why is this true?  (view the website on superposition of waves from week 4 for help)