By Paul C. W. Davies, David S. Betts (auth.)
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Extra info for Quantum Mechanics
Since x = A sin(wt + cp), it follows that 38 Wave mechanics 2 dx = wA cos (wt +
In both cases y increases and more energy levels appear. e. for Voa2 < n 2 h2 /8m, can be traced to the Heisenberg uncertainty principle. Being confined to a region of size ~ a the particle experiences a momentum uncertainty Finite square well 25 /lp ~ h/a, which for an otherwise free particle corresponds to an energy (/lp)2/2m ~ h2/2ma 2. If this is greater than the depth of the well Vo then no bound state will be possible. The well will not be strong enough to overcome the irreducible quantum agitation of the particle.
2 Radial position probability density for the electron in the ground state of the hydrogen atom. The most probable position is ao, and the average position is 3ao/2. The probability declines exponentially at large r. so the probability of the electron being in the spherical shell between rand r + dr is 41tr21 Uo 12 dr. The radial probability density 41tr21 Uo 12 is plotted in Fig. 2. It has a maximum at r = ao. The constant ao is therefore the most probable radial distance of the electron from the nucleus and is known as the Bohr radius because it was originally introduced by Bohr in his atomic model.
Quantum Mechanics by Paul C. W. Davies, David S. Betts (auth.)