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I´m not sure if my way of tackling a question, probably it's a trivial problem, but it's important for me to get it right so any help will be greeted.

The question is as follows:

Problem:consider a particle in a one-dimensional system. The wave function ψ(x) is as follows:

ψ(x)= 0 for (-∞<x<0),

ψ(x)= 1/√a for (0<x<a)

ψ(x)= 0 for (a<x<∞)

i) if the kinetic energy is measured what is the most probable value?

ii) which values of the momentum can never be found when measuring it?

My reasoning:

i) I use the operator for kinetic energy: K= -[itex]\frac{h^2}{2m}[/itex][itex]\frac{∂^2}{∂x^2}[/itex]

which when applied: ∫ψ(x)*Kψ(x)dx gives me zero.

If this was right I assume the most probable value of the kinetic energy is zero.

ii) I have no clue whatsoever what the question means.

Thanks and forgive my bad english, regards from Spain!

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# Free particle in one dimension

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