Note this is a Physics/Calculus question. A particle is described by the wave function: where L=2mm a) Sketch...

Hello!

The probability density is the square of the absolute value of a wave function, in our case it is for positive x's and  for negative x's.

The integral over the real axis of a probability density must be (the total probability). From this statement we can find

So really

Hello!

The probability density is the square of the absolute value of a wave function, in our case it is for positive x's and  for negative x's.

The integral over the real axis of a probability density must be (the total probability). From this statement we can find

So really (b)

(c) the probability of finding the particle within 1 mm of the origin is the integral of the probability density from to It is evidently

which is really 63.2%.

(a), (d) look at the graph at https://www.desmos.com/calculator/mmija615t1

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