Tunneling effect, quantum mechanical

Figure 3.5 Graphical representation of the quantum mechanical tunnelling effect between tip and sample. The probability P of a particle with kinetic energy E tunnelling through a potential barrier cf> is shown as a function of sample-tip separation z.

As shown below there is reason to think that the barrier has a finite height of V0 = 2072 cm-1, so that there is a certain probability that the molecule will invert during the course of its vibrations. It is important to note that in both the ground state (v = 0) and the first excited state (v = 1) of the vibrational mode considered here, the energy of the molecule is lower than the potential barrier. Inversion of ammonia in its lowest vibrational states is therefore classically forbidden. Since inversion as a (hindered) vibrational mode is spectroscopically observed therefore means that it is due to a quantum-mechanical tunnelling effect. 

These predictions can provide an experimental test of the mechanism for quantum-mechanical tunneling effects on electron transfer processes in solution and in glasses over a wide temperature range. 

The reason that a compound ion can be field dissociated can be easily understood from a potential energy diagram as shown in Fig. 2.23. When r is in the same direction as F, the potential energy curve with respect to the center of mass, V(rn) is reduced by the field. Thus the potential barrier width is now finite, and the vibrating particles can dissociate from one another by quantum mechanical tunneling effect. Rigorously speaking, it... 

The underlying principles of STM are essentially very simple indeed. If a sharp metal tip is placed within a distance, dT> of a few A from a conducting sample surface and a bias voltage, Uz, is applied between tip and surface, a tunnelling current. It, will be established between tip and surface due to a quantum mechanical tunnelling effect that is generated under conditions... 

The ability of a particle to penetrate into a classically forbidden region is the basis of the quantum mechanical tunnel effect. Consider a particle for which the potential function looks like that in Fig. 21.6. Two regions of low potential energy are separated by a... 

Example 1.15 For levels 10 meV below the ionization limit, (1.46) gives Eo > 1.7 X 10 V/m for the ionizing external field. However, because of the quantum-mechanical tunnel effect the fields required for complete ionization are even lower. 

T. Miyazaki et al. Japan Quantum mechanical tunneling effect for hot tritium reaction... 

Some New Aspects Related to Hot Atom Chemistry 24.8.3.1 Quantum Mechanical Tunneling Effect... 

It is well known that at very low temperatures quantum mechanical tunneling effect plays a part in the chemical reaction of hydrogen. Miyazaki and coworkers (Fujitani et al. 1991 ... 

Finally, we note that quantum mechanical tunneling effects may also be incorporated through the use of path integral techniques [14]. These effects are believed to be important in electron transfer processes in condensed phases and proteins [15-16]. 

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