The wave function of a particle of mass M confined in an infinite one-dimensional square well of width L = nm, is:

Y(x) = (2/L)^1/2 sin(3px/L) for 0 < x < L
Y(x) = 0 everywhere else.

a) What is the mass of the particle? First give Mc² in eV, then M in kg.

Mc² = eV   
M    = kg    

b) Use P(x) to represent the probability density. The probability that the particle is between x and x+dx is P(x)dx when dx is small. Suppose that dx = 0.01 L. (That is, dx is 1% of the width of the well.) For how many values of x does P(x)dx = 0.01?

P(x)dx = 0.01 for values of x.

c) What is the largest value of x for which P(x)dx = 0.01?

x = nm