1. coordinate /re

2. coordinate /re

3. coordinate /re

4. coordinate /re

5. coordinate /re

6. Morse Potential

7. Correspondence Principle (Bohr, 1923)
“In the limit of high energies and small energy changes, i.e. in the limit of large quantum numbers, quantum theory must converge to classical theory !”
Examples:
H atom: En  1/n2 Energy spacing between adjacent levels En  1/n2 - 1/(n+1)2 For n  : En  0 Classical result: continuous energy solutions allowed
A light field can be described by classical electrodynamics, if the number of photons N >> 1
At high excitation energies in the HO (i.e., high v), the probability density looks similar to the classical HO
At high quantum numbers, the portion of the wave function outside the classically allowed region decreases with increasing v  consistent with correspondence principle: classical behavior at high quantum numbers

8. Spherical Coordinates
< from Simon & McQuarrie, MathChapter D >

9. Angular Momentum Operators