The classical energy (Hamiltonian) is
(7.4) |
The quantum Hamiltonian operator is thus
(7.5) |
And we thus have to solve Schrödinger’s equation
(7.6) |
In order to treat this equation it is better to remove all the physical constants, and go over to dimensionless coordinates
(7.7) |
Quiz What is the dimension of ? and of ? (The dimension of is .)
When we substitute these new variables into the Schrödinger equation we get, using
(7.8) |
that ( )
(7.9) |
Cancelling the common factor we find
(7.10) |