Order of Magnitude Estimates from the HUP (25 pts)

 

A particle of mass m is subject to a radially symmetric potential (in three dimensions) of the form

 

where if and if . Figure 3 illustrates the potential.

  
Figure 3: Generic potential

• Potential Energy
• Kinetic Energy
• Minimum Total Energy and Contributions
• Energy of Confinement
• Balance between Kinetic and Potential Energy
• Correspondence Principle
• Make Your own Estimate of the Energy and Size of the Hydrogen Atom