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## Homework Statement

At the instant t=0, there's a system with 1000 particles in a box of length a. It is known that 100 have energy 4E1 and 900 have energy 225E1, where E1 is the energy of the fundamental state.

i) Build a wave function that can represent the state of a particle

ii) How many particles are in the right half of the well? [a/2 , a]

## Homework Equations

i) [itex]\Psi(x,t) = \Sigma C_{n} \varphi_{n} (x) e^{-i n^{2}wt} [/itex] (1)

[itex]P(E_{n}) = |C_{n}|^{2} [/itex] (2)

ii) [itex] P(t) = \int |\Psi|^{2}| dx [/itex] (3)

[itex]Number of particles = N_{total} P(t) [/itex] (4)

## The Attempt at a Solution

i) [itex]\Psi (x,t) =\frac{1}{3} \sqrt{\frac{2}{a}} sin(\frac{4 \pi x}{a}) e^{i 16 wt} + \frac{3}{\sqrt{10}} \sqrt{\frac{2}{a}} sin(\frac{225 \pi x}{a}) e^{i 50625 wt} [/itex]

ii) I need to know if the formula (4) is right

Thanks in advance.

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