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Chapter 4: Q48E (page 137)
The p0 is a subatomic particle of fleeting existence. Data tables don't usually quote its lifetime. Rather, they quote a "width," meaning energy uncertainty, of about 150MeV. Roughly what is its lifetime?
The lifetime is .
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The position of a neutron in a nucleus is known within an uncertainty of -5x10-13 m. At what speeds might we expect to find it moving?
An electron in an atom can "jump down" from a higher energy level to a lower one, then to a lower one still. The energy the atom thus loses at each jump goes to a photon. Typically, an electron might occupy a level for a nanosecond. What uncertainty in the electron's energy does this imply?
Because we have found no way to formulate quantum mechanics based on a single real wave function, we have a choice to make. In Section 4.3,it is said that our choice of using complex numbers is a conventional one. Show that the free-particle Schrodinger equation (4.8) is equivalent to two real equations involving two real functions, as follows:
and
where is by definition . How is the complex approach chosen in Section4.3more convenient than the alternative posed here?
The uncertainty in the position of a baseball of mass.What is the minimum uncertainty in its speed?
In Exercise 45, the case is made that the position uncertainty for a typical macroscopic object is generally so much smaller than its actual physical dimensions that applying the uncertainty principle would be absurd. Here we gain same idea of how small an object would have♦ to be before quantum mechanics might rear its head. The density of aluminum is , is typical of solids and liquids around us. Suppose we could narrow down the velocity of an aluminum sphere to within an uncertainty ofper decade. How small would it have to be for its position uncertainty to be at least as large asof its radius?
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