Create an organized data sheet for each of the following quantum mechanical systems:
1D particle in a box
3D particle in a box
ideal harmonic oscillator
2D rigid rotor
3D rigid rotor
hydrogen-like atom
For each system:
– give the general formula for the wavefunction
– identify all variables and give their allowed values when appropriate
– give the general formula for the energy of the system
– identify all variables and give their allowed values when appropriate
– State whether the (angular) momentum of the system is solvable analytically
– give a generic equation or a result for the momentum
– state any unusual considerations (for example, maybe only the square of the angular
momentum can be solved analytically. If so, does it allow a value to be
determined for the total angular momentum?
– identify all variables and give their allowed values when appropriate
– give a summary of any quantum numbers that are needed by the system and give their
allowed values.