70Then weimpose twosimultaneousperturbations: anelectric field in
the and a magneticfield which is given by the
vectorpotential Ignore the magnetic moment of the
electron.Calculate how the states are altered by these simultaneous
perturbations.
5.50 Hydrogen in Capacitor (Maryland, Michigan
State)A hydrogen atom inits ground state isplaced between the parallel plates
of a capacitor. Fortimest< 0, no voltage is applied. Starting at an
electric field is applied,where is aconstant. Derive the
formula for the probabilitythat theelectron ends up instate due to this
perturbation.Evaluate theresult for
a) a state
b) a state5.51 Harmonic Oscillator in Field (Maryland,
Michigan State)
A particle ofmass and charge moves in onedimension. It is attached
to a spring of constant and is initially in theground state of the
harmonicoscillator. Anelectric field isswitched onduring theinterval
where is a constant.
a) What is the probability ofthe particle ending up in the state?
b) What is the probability of the particle ending up in the state?5.52 of Tritium (Michigan State)
Tritium is anisotope ofhydrogen with oneproton and two neutrons. A
hydrogen-like atom isformed with an electronbound to thetritium nucleus.
The tritiumnucleus undergoes decay, and thenucleuschanges its charge
state suddenly to andbecomes an isotope ofhelium. If the electron is
initially in the ground state in thetritiumatom, what is the probability
that theelectron remains in the ground stateafter thesudden -decay?
PROBLEMS