Particles in 3D Potentials and the Hydrogen Atom5P(r)04a001rr = a0zxLLL()222228zyxnnnnnnmLhEzyx++⋅=)()()(),,(zyxzyxϕϕϕψ=oa/r3oea1)r(−=πψ2613neV.En−=
OverviewOverviewz3-Dimensional Potential WellzProduct WavefunctionszConcept of degeneracyzEarly Models of the Hydrogen AtomzPlanetary ModelzSchrödinger’s Equation for the Hydrogen AtomzSemi-quantitative picture from uncertainty principle zGround state solution*zSpherically-symmetric excited states (“s-states”)*z*contain details beyond what we expect you to absorb
has intentionally blurred sections.
Sign up to view the full version.
Quantum Particles in 3D PotentialsQuantum Particles in 3D PotentialszOne consequence of confining a quantum particle in two or three dimensions is “degeneracy”-- the occurrence of several quantum states at the same energy level.zSo far, we have considered quantum particles bound in one-dimensional potentials. This situation can be applicable to certain physical systems but it lacks some of the features of many “real” 3D quantum systems, such as atoms and artificial quantum structures:(www.kfa-juelich.de/isi/)A real (3D) “quantum dot”zTo illustrate this important point in a simple system, we extend our favorite potential -- the infinite square well --to three dimensions.