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Chapter 8: Q71E (page 344)

Repeat example 8.6 but assume that the upper state is the 2p12rather than the2p32

Short Answer

Expert verified

The 1s12and 2p12states are both split into two levels.

Step by step solution

01

 Step 1: Concept of the ordering Rule for Z- projection.

The ordering rule for the quantum number of the z-projection of the total angular momentum mjis:mj=-j,-j+1,....,j-1,j

Here Jis the quantum number for the total angular momentum.

02

Determine the state of two levels which is split

The J 's for the1s12 and2p12states are both12since that's what the subscripts of the states are. Consequently, the's are given by:

mj=-12,+12

The 1s12and2p12states are both split into two levels.

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Most popular questions from this chapter

Question: What if electrons were spin32 instead of spin 12. What would be Z for the first noble gas?

The angles between S and μSand between L and μLare 180o. What is the angle between J and μJ in a2p32state of hydrogen?

What angles might the intrinsic angular momentum vector make with the z-axis for a deuteron? (See Table 8.1)

Exercise 44 gives an antisymmetric multiparticle state for two particles in a box with opposite spins. Another antisymmetric state with spins opposite and the same quantum numbers is ψn(x1)↓n2(x2)↑−ψnn(x1)↑ψn(x2)↓

Refer to these states as 1 and 11. We have tended to characterize exchange symmetry as to whether the state's sign changes when we swap particle labels. but we could achieve the same result by instead swapping the particles' stares, specifically theandin equation (8-22). In this exercise. we look at swapping only parts of the state-spatial or spin.

(a) What is the exchange symmetric-symmetric (unchanged). antisymmetric (switching sign). or neither-of multiparticle states 1 and Itwith respect to swapping spatial states alone?

(b) Answer the same question. but with respect to swapping spin states/arrows alone.

(c) Show that the algebraic sum of states I and II may be written(ψn(x1)ψn'(x2)−ψn'(x1)ψn(x2))(↓↑+↑↓)

Where the left arrow in any couple represents the spin of particle 1 and the right arrow that of particle?

(d) Answer the same questions as in parts (a) and (b), but for this algebraic sum.

(e) ls the sum of states I and 11 still antisymmetric if we swap the particles' total-spatial plus spin-states?


(f) if the two particles repel each other, would any of the three multiparticle states-l. II. and the sum-be preferred?

Explain.

The subatomic omega particle has spin s=32. What angles might its intrinsic angular in momentum vector make with the z-axis?
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