d) Because the particle is stuck inside the well, the quadratic is only valid when 0 ≤ x ≤ 1. Outside the well, f(x) = 0. Update f(x) by writing it as a piece-wise function with this new information. The diagram below might be helpful. you can just say f(x) = ax2 +bx+c for the quadratic section. e) We call f(x) the quantum wave function; however, f itself doesn’t tell us much about the particle’s behavior. Instead, physicists use f(x) 2 = (f(x))2 = f(x)·f(x) since it is proportional to the probability of finding the particle near that x-value. Using your answer from part (d), find f(x) 2 .

d) Because the particle is stuck inside the well, the quadratic is only valid when 0 ≤ x ≤ 1. Outside the well, f(x) = 0. Update f(x) by writing it as a piece-wise function with this new information. The diagram below might be helpful. you can just say f(x) = ax2 +bx+c for the quadratic section. e) We call f(x) the quantum wave function; however, f itself doesn’t tell us much about the particle’s behavior. Instead, physicists use f(x) 2 = (f(x))2 = f(x)·f(x) since it is proportional to the probability of finding the particle near that x-value. Using your answer from part (d), find f(x) 2 .

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter6: Exponential And Logarithmic Functions

Section6.4: Graphs Of Logarithmic Functions

Problem 60SE: Prove the conjecture made in the previous exercise.

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