A particle is introduced into the well at t = 0 and its initial wavefunction cor

Question

A particle is introduced into the well at t = 0 and its initial wavefunction corresponds to
the particle having equal probability to be found anywhere between x = 0 and x = L .

iv) Write down a correctly normalised expression for the wavefunction, (x,0) ,
that correctly describes this initial state.

v) What does it mean to say that the n(x) must form a complete set, and what does
this imply for writing any wavefunction in terms of the n(x) ?

vi) For this initial state, write (x,0) as a sum over n(x), evaluating all terms in the
summation, and hence derive the probabilities for measuring the different
possible En values.

vii) Hence also write (as an infinite series) the wavefunction (x,t)
describing how this initial state evolves with time.

ps:actually there is part I of these questions but it already been answered. here are the information about part I question (just for note):

An infinite potential well is an idealisation that corresponds to the potential, V(x) = 0
in a limited range, say from x = 0 to x = L and V(x) being infinite outside this range.
Solutions to the one-dimensional Schrödinger’s time independent equation for a particle
inside such a well have the form n(x) = Ansin(knx) .

Explanation / Answer

wave

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