I have done all sections up to part d), which is the part I am having trouble wi

Question

I have done all sections up to part d), which is the part I am having trouble with just wondering if someone could look at my wroking for it, as I think it not an eignesate.

Consider a particle of mass m in an infinite, one-dimensional, square well potential extending from x = 0 to x = L. The allowed values of the energy, and the corresponding normalised wavefunctions, in the position representation, are given by 2mL n1,2,3,4,.. Consider the following linear superposition of the ground state and the first excited state: (11) + 12). = (a) what is the position-representation wavefunction, ?(z) (zk)? Express your (b) What is the corresponding probability density as a function of ? Express your (c) What probability that the particle wil be found in the left half of the box, i.e. (d) Is the state lp) an eigenstate of momentum? result as a function of r and L result as a function of r and L with 0

Explanation / Answer

your work is correct. As eigen state is asked, the answer will be cos(pix/L)+2cos(2pix/L). the value which you are referring will be the eigen value.

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