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# Free Particles: Wavefunction, Momentum, and Probability

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At t=0, the wavefunction of a free particle is:

psi(x,0) = {(sqrt b/2*pi)sin(bx) for |x|<((2*pi)/b)
{0 for |x|> or = ((2*pi)/b))

a) What is the probability of finding the particle in the interval 0 less than or equal to x less than or equal to pi/2b?

b) What is the momentum amplitude for this wavefunction?

c) For what value of the momentum is the momentum probability maximum?

d) What is the probability for finding the momentum in an interval dp around (h_bar)b?

https://brainmass.com/physics/wavefunction/free-particles-wavefunction-momentum-probability-556874

#### Solution Preview

The solution is attached below in two files. The files are identical in content, only differ in format. The first is in MS Word format, while the other is in Adobe pdf format. Therefore you can choose the format that is most suitable to you.

The wave function in position space is:
(1.1)
By definition, the probability to find the particle between x and x+dx is:
(1.2)
So the probability to ...

#### Solution Summary

The wavefunction, momentum and probability for free particles are given. The momentum amplitude for the wavefunction is discussed.

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