Problems
The first two questions are for the one-dimensional particle in a box.
10.1 What is the wavelength of the first excited state state in terms of L?
10.2 If the length Lis 8 Å, what is the wavelength of the (a) ground state and (b) second excited
state of an electron?
10.3 Write (but do not solve) an integral expression for the average value, or expectation value,
of (a) the momentum and (b) the momentum squared for the ground state.
10.4 Write (but do not solve) an integral expression for the probability of finding the particle
between x=0 and x=L/4.
10.5 Write (but do not solve) an integral expression for the average value, or expectation value,
of x^2 for the ground state.
218 PART 2 QUANTUM MECHANICS AND SPECTROSCOPY
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