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Chapter 8: Q2CQ (page 338)
Does circulating charge require both angular momentum and magnetic? Consider positive and negative charges simultaneously circulating and counter circulating.
No, the circulating charge does not require both angular momentum and magnetic.
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The general form for symmetric and antisymmetric wave functions is but it is not normalized.
(a) In applying quantum mechanics, we usually deal with quantum states that are "orthonormal." That is, if we integrate over all space the square of any individual-particle function, such as, we get 1, but for the product of different individual-particle functions, such as, we get 0. This happens to be true for all the systems in which we have obtained or tabulated sets of wave functions (e.g., the particle in a box, the harmonic oscillator, and the hydrogen atom). Assuming that this holds, what multiplicative constant would normalize the symmetric and antisymmetric functions?
(b) What valuegives the vectorunit length?
(c) Discuss the relationship between your answers in (a) and (b)?
Question: Solving (or attempting to solve!) a 4-electron problem is not twice as hard as solving a 2-electrons problem. Would you guess it to be more or less than twice as hard? Why?
In its ground state, nitrogen's 2p electrons interact to produce . Given Hund's rule, how might the orbit at angular momenta of these three electrons combine?
Exercise 45 refers to state I and II and put their algebraic sum in a simple form. (a) Determine algebraic difference of state I and state II.
(b) Determine whether after swapping spatial state and spin state separately, the algebraic difference of state I and state II is symmetric, antisymmetric or neither, and to check whether the algebraic difference becomes antisymmetric after swapping spatial and spin states both.
Is intrinsic angular momentum "real" angular momentum? The famous Einstein-de Haas effect demonstrates it. Although it actually requires rather involved techniques and high precision, consider a simplified case. Suppose you have a cylinder in diameter hanging motionless from a thread connected at the very center of its circular top. A representative atom in the cylinder has atomic mass 60 and one electron free to respond to an external field. Initially, spin orientations are as likely to be up as down, but a strong magnetic field in the upward direction is suddenly applied, causing the magnetic moments of all free electrons to align with the field.
(a) Viewed from above, which way would the cylinder rotate?
(b) What would be the initial rotation rate?
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