Consider the electron wave function
a. Determine the normalization constant c. Your answer will be in terms of L.
b. Draw a graph of over the interval -L x 2L.
c. Draw a graph of over the interval -L x 2L. d. What is the probability that an electron is in the interval 0 x L/3?
The Value of Probability is.
Sub part (a) step1:
For the probability interpretation of to make sense the wave function must satisfy the following equation
The above integrals is expanded as follows
The wave function is defined only in the region therefore substitute csin for thye second integral and zero for the rest of regions
consider the following trigonometric relation
Hence substitute for sin2 AND SOLVE FOR C
THEREFORE, THE VALUE OF PROBABILITY IS 40.2%
An experiment finds electrons to be uniformly distributed over the interval 0 cm x 2 cm, with no electrons falling out-side this interval.
a. Draw a graph of 0 c1x2 0 2 for these electrons.
b. What is the probability that an electron will land within the interval 0.79 to 0.81 cm?
c. If 106 electrons are detected, how many will be detected in the interval 0.79 to 0.81 cm?
d. What is the probability density at x = 0.80 cm?
A particle is described by the wave function c1x2 = b cex/L x … 0 mm ce-x/L x Ú 0 mm where L = 2.0 mm.
a. Sketch graphs of both the wave function and the probability density as functions of x.
b. Determine the normalization constant c.
c. Calculate the probability of finding the particle within 1.0 mm of the origin. d. Interpret your answer to part b by shading the region representing this probability on the appropriate graph in part a
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