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Chapter 5: Q7CQ (page 186)
We say that the ground state for the particle in a box has nonzero energy. What goes wrong with in equation 5.16 if n = 0 ?
If n = 0 in equation of , this would make locating our particle difficult, meaning that it no longer exists.
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Quantization is an important characteristic of systems in which a particle is bound in a small region. Why "small," and why "bound"?
Because protons and neutrons are similar in mass, size, and certain other characteristics, a collective term, nucleons, has been coined that encompasses both of these constituents of the atomic nucleus. In many nuclei, nucleons are confined (by the strong force, discussed in Chapter) to dimensions of roughfemtometers. Photons emitted by nuclei as the nucleons drop to lower energy levels are known as gamma particles. Their energies are typically in the Merange. Why does this make sense?
Figure 5.15 shows that the allowed wave functions for a finite well whose depth was chosen to be.
(a) Insert this value in equation (5-23), then using a calculator or computer, solve for the allowed value of , of which there are four.
(b) Usingfind corresponding values of E. Do they appear to agree with figure 5.15?
(c) Show that the chosenimplies that .
(d) Definingandto be 1 for convenience, plug your and values into the wave function given in exercise 46, then plot the results. ( Note: Your first and third values should correspond to even function of z, thus using the form with, while the second and forth correspond to odd functions. Do the plots also agree with Figure 5.15?
a) Taking the particle鈥檚 total energy to be 0, find the potential energy.
(b) On the same axes, sketch the wave function and the potential energy.
(c) To what region would the particle be restricted classically?
A particle is described by the wave function
(a) Show that the normalization constantis correct.
(b) A measurement of the position of the particle is to be made. At what location is it most probable that the particle would be found?
(c) What is the probability per unit length of finding the particle at this location?
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