Chapter 8: Q5CQ (page 338)
The neutron comprises multiple charged quarks. Can a particle that is electrically neutral but really composed of charged constituents have a magnetic dipole moment? Explain your answer.
Yes, an electrically neutral particle composed of charged constituents has a magnetic dipole moment.
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Angular momenta and interact so that they obey the strict quantum mechanical rules for angular momentum addition. If and what angles between and allowed?
The angles between S and and between L and are 180o. What is the angle between J and in astate of hydrogen?
The total-spin singlet state for two electrons has one spin up and one down, but one of the triplet states does. too. What is the difference?
Here we consider adding two electrons to two "atoms," represented as finite wells. and investigate when the exclusion principle must be taken into account. In the accompanying figure, diagram (a) shows the four lowest-energy wave functions for a double finite well that represents atoms close together. To yield the lowest energy. the first electron added to this system must have wave function and is shared equally between the atoms. The second would al so have function and be equally shared. but it would have to be opposite spin. A third would have function B. Now consider atoms far a part diagram(b) shows, the bumps do not extend much beyond the atoms - they don't overlap-and functions and approach equal energy, as do functions and . Wave functionsandin diagram (b) describe essentially identical shapes in the right well. while being opposite in the left well. Because they are of equal energy. sums or differences ofandare now a valid alternative. An electron in a sum or difference would have the same energy as in either alone, so it would be just as "happy" inrole="math" localid="1659956864834" , or- B. Argue that in this spread-out situation, electrons can be put in one atom without violating the exclusion principle. no matter what states electrons occupy in the other atom.
Two particles in a box have a total energy .
(a) Which states are occupied?
(b) Make a sketch ofversusfor points along the line.
(c) Make a similar sketch of.
(d) Repeat parts (b) and (c) but for points on the line
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