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Chapter 40.1, Problem 40.1QQ
To determine

The value of x where the particle is most likely to be found.

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The wave function of a particle in a one-dimensional box of width L is u(x) = A sin (7x/L). If we know the particle must be somewhere in the box, what must be the value of A?
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Consider a particle in the first excited state of an infinite square well of width L. This particle has wavefunction *60 = √ (7) 4₂(x) sin L for -L/2 ≤ x ≤ L/2, and 2(x) = 0 elsewhere. a) What is the value of the energy of this particle, E₂? b) What is the probability density function, p, for this particle? c) At what values of does the probability density vanish? d) What is the probability of finding this particle in the interval 0 ≤ x ≤ L/8?
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