Consider a particle of mass m that can move in a one-dimensional box of size L...

Consider a particle of mass m that can move in a one-dimensional box of size L with the edges of the box at x=0 and x = L. The potential is zero inside the box and infinite outside.

You may need the following integrals:

∫ 0 1 d y sin ⁡ ( n π y ) 2 = 1 / 2 , for all integer n

∫ 0 1 d y sin ⁡ ( n π y ) 2 y = 1 / 4 , for all integer n

∫ 0 1 d y sin ⁡ ( n π y ) 2 y 2 = 1 6 − 1 16 π 2 , for all integer n

(a) Write down the time-independent Schrodinger equation describing the system, and determine whether ψ = sin ⁡ ( 2 π x / L )is an energy eigenstate by checking whether it satisfies the Schrodinger equation. If it is an energy eigenstate, what is the energy? [10 pts]

(b) Suppose we measure the position of the particle in the state in part (a) repeatedly and average the results. Determine the result. [10 pts]

(c) What are the most likely places to find the particle in a single measurement if it is in the state in part (a)? [10 pts]

Expert Solution

genius_generous answered 2 years ago

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