Classical Versus Quantum Mechanical Orbits

why 1s orbital is spherical? And why orbital of earth is not spherical,however in both cases particle is revolving around nucleus and sun respectively?
- Ankit (age 17)
Sagar,mp India

Dear Ankit,

The 1s orbital you refer to is the lowest energy quantum mechanical solution to Schoedinger's equation.   It is not a classical orbit in the sense that it does not describe the path of an electron revolving around a nucleus but a probability of finding the electron at a particular point in space.   That particular quantum state carries no angular momentum, others do.  So, in that sense it has no relation to a classical orbit where there is always some angular momentum.  The classical Keplerian orbits of a gravitational 1/r² force are ellipses with the the Sun at one of the focii. 

LeeH

 

p.s. To make a classical-like Keplerian orbit for something small, you have to put together many quantum states with slightly different energies. /mw

(published on 06/07/2013)