Question

Q5 (15 points) Quantum Queries A particle of mass m is placed in a one-dimensional infinite square well potential of width L. [2] (a) What is the zero-point energy of a particle placed in this well? [4] (b) Determine the probability P_n(0 < x < L/a) that a particle in the nth energy state ?_n(x) is observed to be in a region 1/a of the width of the well. [5] (c) For what value of n is this probability the largest? What does your answer become if the region is chosen to be 1/3 the size of the box? [2] (d) What does the probability in part (b) become as n gets large? [2] (e) If the particle in part (b) were classical (no quantum physics), what would be the probability that it would be confined to a region 1/a of the width of the well? How does this compare to your answer in part (d)?

          Q5 (15 points)

Quantum Queries

A particle of mass m is placed in a one-dimensional infinite square well potential of width L.

[2] (a) What is the zero-point energy of a particle placed in this well?

[4] (b) Determine the probability P_n(0 < x < L/a) that a particle in the nth energy state ?_n(x) is observed to be in a region 1/a of the width of the well.

[5] (c) For what value of n is this probability the largest? What does your answer become if the region is chosen to be 1/3 the size of the box?

[2] (d) What does the probability in part (b) become as n gets large?

[2] (e) If the particle in part (b) were classical (no quantum physics), what would be the probability that it would be confined to a region 1/a of the width of the well? How does this compare to your answer in part (d)?

Q5 (15 points)

Quantum Queries

A particle of mass m is placed in a one-dimensional infinite square well potential of width L.

[2] (a) What is the zero-point energy of a particle placed in this well?

[4] (b) Determine the probability Pn(0 < x < L/a) that a particle in the nth energy state ?n(x) is observed to be in a region 1/a of the width of the well.

[5] (c) For what value of n is this probability the largest? What does your answer become if the region is chosen to be 1/3 the size of the box?

[2] (d) What does the probability in part (b) become as n gets large?

[2] (e) If the particle in part (b) were classical (no quantum physics), what would be the probability that it would be confined to a region 1/a of the width of the well? How does this compare to your answer in part (d)?

Added by Joaquin R.

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