1. If a cricket ball is to be diffracted as a de Broglie wave at the wickets, with what velocity should it hit the wickets?

2. A 1-dimensional system consisting of a single particle has the state function,

Find the normalization constant N. Estimate the probability that the position, x , of the particle is between 2.999 and 3.000 units.

3. Derive the following commutators:

4. Write down the most general solution of the Hamiltonian for the 1-dimensional particle in a box. Apply boundary conditions to obtain the eigen functions. Check if these functions are eigen functions of the momentum operator. Comment.

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