Max-Planck-Institut für Quantenoptik (MPQ), Laser Spectroscopy Division

The electron wavefunction of a bound state in the hydrogen atom can be written as Rnl(r) Ylm(theta,phi). The extension of the electron cloud in a given direction, that is specified by the angles theta and phi, may be defined by a certain value of Rnl(r) (e.g. the first zero or the first maximum). In this case the value of Ylm(theta,phi), that is independent of r, scales the extension of the cloud in the direction (theta,phi). The surface defined by r(theta,phi) = | Ylm(theta,phi) |2 then gives the shape of the electron cloud up to a scaling factor that depends on chosen value of Rnl(r) which marks the "edge" of the cloud. We can therefore visualize the shape of the oscillating atom by calculating the surface for a mixed state a1Yl1m1(theta,phi)+a2Yl2m2(theta,phi). Since the two wavefuntions have different energies the absolute modulus of the mixture will depend on time.
 

The following MPEG samples show these oszillating wavefunctions.

The z-axes is oriented almost vertical but slightly tilted on the top towards the observer. Pi transitions (m1-m2=0) oscillate along the z-axes while sigma transition (m1-m2=1) rotate about the z-axes. The quadrupole 1S-2S transition has a different symmetry. 

The 1S - 2S  transition 1s2s.mpg (21.3 kB)


   

The l=1, m=0  to  l=0, m=0  transition y10y00.mpg (31.7 kB)


 

The l=2, m=1  to  l=1, m=1  transition y21y11.mpg (43.8 kB)


 

The l=1, m=1  to  l=0, m=0  transition y11y00.mpg (36.8 kB)


 

The l=2, m=1  to  l=1, m=0  transition y21y10.mpg (48.7 kB)


 

Other hydrogen animations are available here:

    The l=6, m=0  to  l=5, m=0  transition y60y50.mpg (25.1 kB)
    The l=6, m=3  to  l=5, m=2  transition y63y52.mpg (66.0 kB)
    The l=6, m=5  to  l=5, m=5  transition y65y55.mpg (44.1 kB)
    The l=7, m=2  to  l=7, m=1  transition y72y71.mpg (52.7 kB)

Quadrupole transitions with delta m=2:
    The l=4, m=2  to  l=2, m=2  transition y42y22.mpg (45.3 kB)
    The l=4, m=1  to  l=2, m=-1 transition y41y2-1.mpg (64.7 kB)
    The l=3, m=0  to  l=2, m=2  transition y30y22.mpg (56.6 kB)

1s2s.avi.zip (537 kB) shows a complete measuring cycle: Excitation to the 1S state by using two photons from oposite directions so that the first order doppler shift cancels. Here it is shown as a complete transition (driven by a pi pulse) while in reality the excitation is much less. Then there is a time delay to select the slow atoms to reduce the second order doppler shift. An electric field that is applied downstream the flow of excited atoms mixes the metastable 2S state with the fast decaying 2P state. This causes the emission of a photon in an arbitrary direction that we use to detect weather the 1S - 2S transition frequency was chosen correctly.

Go back to the MPQ homepage or the Hänsch group homepage. 

Last modified 13.3.1998