Probability densities quantum-mechanical tunneling

The wave functions for u = 0 to 4 are plotted in figure 6.20 the point where the function crosses through zero is called a node, and we note that the wave function for level v has v nodes. The probability density distribution for each vibrational level is shown in figure 6.21, and the difference between quantum and classical behaviour is a notable feature of this diagram. For example, in the v = 0 level the probability is a maximum at y = 0, whereas for a classical harmonic oscillator it would be a minimum at v = 0, with maxima at the classical turning points. Furthermore the probability density is small but finite outside the classical region, a phenomenon known as quantum mechanical tunnelling. 

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