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The sides of a one dimensional quantum box (1-D) are in x=0, x=L. The probability of...

The sides of a one dimensional quantum box (1-D) are in x=0, x=L. The probability of observing a particle of mass m in the ground state, in the first excited state and in the 2nd excited state are 0.6, 0.3, and 0.1 respectively

a) If each term contributing to the particle function has a phase factor equal 1 in t=0. What is the wave function for t>0?

b) what is the probability of finding the particle at the position x=L/3 and x=L/2 at time t=0, using the wave function of a)?

c) what is the expected value of the energy that a measurement could have at t=mL^2 /hπ?

thanks

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