Imaging Experiences

Born-Interpretation of the Wavefunction

As matter is examined on an ever more microscopic scale, familiar bulk scale expectations are replaced with more bizarre descriptions of behavior. In particular, our every day experience of particle-like behavior (objects having definite positions and momenta) is shown to be an incorrect representation of the way sub atomic particles move. Instead, wavefunctions are used to discuss the properties of a quantum mechanical system. A physical interpretation of the wavefunction was proposed by Max Born and incorporated as part of the Copenhagen interpretation of quantum mechanics. Born proposed that the wave function encapsulates the probabilistic nature of the quantum world. Using a free electron as an example, the square of the amplitude of the wavefunction (or strictly the square modulus of the wavefunction) is the probability density for finding the electron within a particular region of space. Where this gets interesting is when we try and locate the actual, rather than likely position of an electron. Any measurement will record the position of the electron at a definite (within the precision of the measuring device) location. If we were to repeat this measurement under exactly the same conditions on an identical free electron, we would again find the electron at a definite position BUT, not necessarily the same position as the first measurement. If we were to string together a whole series of such measurements we could create a map of individual electron locations, which would represent a probability map for location of any one of the electrons before a measurement is made. Under the Born-interpretation of the wavefunction we cannot say for definite where our free electron will be at a given instant, but we do have an idea of where it is more or less likely to be.

Illustration Using Photoelectron Imaging

In our velocity mapped photoelectron imaging experiments, electrons with the same nascent velocity vector are detected at the same spot on the detector irrespective of their initial position. In the photodetachment process from the hydride anion, [H- + hυ → H(E,v) + e- (p,x,y,z) ], electrons are produced from identically prepared atomic hydride by identically prepared photons. Use of the velocity mapped arrangment effectively means that the photoelectrons are produced from an identical points in momentum space. Each electron is the result of the action of one photon on one anion and is detected as a single event on our detector. This event is recorded as a bright, localized spot on our detector – a particle-like event. However, in our experiments a pulse of anions interacts with a pulse of photons producing a number of electrons. The impact spots due to these seem to be randomly distibuted on the detector. However, accumulating the results over a number of ion/photon pulses builds up a picture of the more and less likely impact locations.

Fig. 1 Image Accumulation: 750 nm H- Detachment 

Fig. 1 shows data collection in action. The panel to the left shows the individual pulses (a single experimental cycle) in an experiment where electrons are detached from atomic hydride at a photon wavelength of 750 nm. Electron impacts on the detector are seen as individual bright spots, a number of which are distributed on the screen. These appear to move on a pulse by pulse basis (in other words the imapct positions change). The right hand panel shows the result of accumulation of a number of cycles. The brighter areas correspond to more electron impacts within the time period of the experiment. Thus the image maps out more or less likely locations for electron location. Interestingly, while the image is clearly circular, the distribution of electrons about a circle of a given radius is non-uniform. The reason for this anisotropic angular distribution of photoelectrons is related to the nature of the original (bound) electronic wavefunction within the hydride atomic anion.