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Quantum Microscope (H Atom Images)

Advance in scanning tunneling microscopes (STM) had revealed the electron clouds surrounding some atoms and molecules. Detailed structure similar to the theoretical pictures of the wave functions (or probability) in atoms has never been imaged until recently in 2013, when the images of hydrogen atom were successfully captured by photoionization microscopy. The theoretical consideration and the novel technique in this experiment are summarized below before showing some pictures of the H atom. This experiment demonstrates that the wave function in Quantum Theory is for real. It is not fancy imagination concocted by theoretical physicists nor a mathematical oddity. See original paper on "Hydrogen Atoms under Magnification" for more detail.

Mathematics on the formation of the H atom image :

The inverse transformation from the parabolic coordinates to Cartesian coordinates is :

x = cos()
y = sin()
z = (2 - 2)/2

At = o where the electron can escape, the x and y components of the velocity would be :

dx/dt = o cos() (d/dt), and
dy/dt = o sin() (d/dt) respectively.

The (d/dt) is determined by the available energy [E - V()] as shown in Figure 13-02n. The value of (d/dt) increases from zero at the edge of the barrier with the probability distribution varies up and down. It is the (d/dt) together with the angular coordinate that traces a circular pattern on the detecting screen (see insert in Figure 13-02p). The intensity on each circle reflects the probability distribution which is proportional to the number of ionized electron having the particular values of (dx/dt), (dy/dt).