Solutions of the Time Independent Schrödinger Equation (TISE)

Background: While, as in Problem 3, many general facts may be derived from the eigenstate expansion, to answer specific questions we need the solutions to the TISE. This problem develops that skill.

This problem will center on the solutions to various limits of the potential sketched in Figure 2.

  
Figure 2: ``Bumpy'' Finite Square Well Potential

• Wavefunctions of the Even States
• Eigenenergies of the Even States
• Limit of an infinite ``bump''
• States with zero curvature
• Limit of infinite walls
• Odd states