Excited Hydrogen Atom Lifetime.
(Submitted by group 3)
We start with the wavefunctions of the ground and first excited state of the hydrogen atom.
The transistion rate is given by the Fermi Golden rule;
We must evaluate equations of the form
Exploiting the symmetry of the wavefunctions we find that the only non-zero element for the z compoent is,
Integrating over all space we find;
For the integrations over x and y we note that all the wavefunctions are even in these variables except for
Our equation for
is as follows;
This yields
This gives a value fore the lifetime of the
and
states as
The
state had matrix elements of 0, this implies that the lifetime is;
This implies that the
state is stable.