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Particle of mass m in a one-dimensional impenetrable box

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A particle of mass m is in a one-dimensional impenetrable box extending from x = 0 to x = a. At t = 0, its wavefunction is given as:

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a) What is the probability for finding the particle in the ground state at t = 0?
b) What is the probability of finding the particle between x = 0 to x = al2 at t = 0?
c) Calculate (a) and (b) for time t.

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A particle of mass m is in a one-dimensional impenetrable box extending from x = 0 to x = a. At t = 0, its wavefunction is given as

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The probability to find the system in state n is the integral of the square of the product of the wave function of the system and the wave function of state n (it's nicer in a formula).
Rewrite the system wavefunction as a linear combination of the particle in a box eigenfunctions, and ...

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