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Chapter 8: Q8CQ (page 338)
Imagine two indistinguishable particles that share an attraction. All other things being equal, would you expect their multiparticle spatial state to be symmetric, ant symmetric, or neither? Explain.
The particles are in close proximity and are represented by a symmetry function.
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To investigate the claim that lowerimplies lower f energy. consider a simple case: lithium. which has twoelectrons and alonevalence electron.
(a)First find the approximate orbit radius, in terms of. of anelectron orbiting three protons. (Refer to Section 7.8.)
(b) Assuming theelectrons shield/cancel out two of the protons in lithium's nucleus, the orbit radius of anelectron orbiting a net charge of just.
(c) Argue that lithium's valence electron should certainly have lower energy in a 25 state than in astale. (Refer Figure 7.15.)
The general rule for adding angular momenta is given in Exercise 66, when adding angular momenta with and
(a) What are the possible values of the quantum number and the total angular momentum .
(b) How many different states are possible and,
(c) What are the values for each of these states?
Question: In the Stern-Gerlach experiment how much would a hydrogen atom emanating from a 500 K ovenbe deflected in traveling 1 m through a magnetic field whose rate of change is 10 T/m?
The wave functions for the ground and first excited states of a simple harmonic oscillator are and. Suppose you have two particles occupying these two states.
(a) If distinguishable, an acceptable wave function would berole="math" localid="1659955524302" . Calculate the probability that both particles would be on the positive side of the origin and divide by the total probability for both being found over all values of,. (This kind of normalizing-as-we-go will streamline things.)
(b) Suppose now that the particles are indistinguishable. Using thesymbol to reduce your work. calculate the same probability ratio, but assuming that their multiparticle wave function is either symmetric or antisymmetric. Comment on your results.
Verify that the normalization constant given in Example 8.2is correct for both symmetric and antisymmetric states and is independent ofand ?
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