The wave function representing a particle's position is g(x)= 17i

Question

The wave function representing a particle's position is g(x)= 17i - (8-7i)x.At what value of x is the probability distribution function minimum?
A)1.05 m
B)-1.05 m
C)7.93 m
D)-7.93 m
E)2.11 m

Quizplus · Accepted Answer

The probability distribution function is given by:

|g(x)|^2 = |17i - (8-7i)x|^2

= (17)^2 + (8-7x)^2

This is a U-shaped curve with the minimum value at the vertex. The x-coordinate of the vertex can be found using:

x = -b/2a

where a = -49 and b = 112.

Thus, x = -112/(-98) = 1.14 m or approximately -1.05 m (rounded to two decimal places).

Since negative values are not physically meaningful for position, the correct answer is B (-1.05 m).