The wave function of a particle of mass m confined in an infinite one-dimensional square well of width L = 0.23 nm, is:
ψ(x) = (2/L)1/2 sin(3πx/L) for 0 < x < L
ψ(x) = 0 everywhere else. The energy of the particle in this state is E = 63.974 eV.
1) What is the rest energy (mc2) of the particle?
ANS: 511133.6 ev
2) P(x) is the probability density.
That is, P(x)dx is the probability that the particle is between x and x+dx when dx is small.
For how many values of x does P(x) = 5 nm-1?
ANS: 6 values of x
3)What is the largest value of x for which P(x) = 5 nm-1?
The Attempt at a Solution
For question 2 i only know its 6 because the question was multiple attempts. i don't know how to get that answer mathematically. I thought that by integrating P(x) squared and then solving for the x's would give me the 6 values of x but its not making sense to me. After i have the 6 values, then the answer to question 3 is just the largest value of x.