Chapter 8: Q31E (page 339)
The subatomic omega particle has spin . What angles might its intrinsic angular in momentum vector make with the z-axis?
Short Answer
Angles that intrinsic angular momentum vector
Chapter 8: Q31E (page 339)
The subatomic omega particle has spin . What angles might its intrinsic angular in momentum vector make with the z-axis?
Angles that intrinsic angular momentum vector
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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)?
Verify that the normalization constant given in Example 8.2is correct for both symmetric and antisymmetric states and is independent ofand ?
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.
(a) Show that, taking into account the possible z-components of J, there are a total of 12 L S coupled states corresponding to 1 s 2 p in Table 8.3.
(b) Show that this is the same number of states available to two electrons occupying 1 s and 2 p if LS coupling were ignored.
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