Q.38

Expert-verifiedFound in: Page 1139

Book edition
4th

Author(s)
Randall D. Knight

Pages
1240 pages

ISBN
9780133942651

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

the normalization constant c is 0.707 mm^{-1/2}

prob=

Thus the probability of finding the particle within 1.0mm for the origin is 63.2%

The expression for the probability of a particle at position x is given from probability density is as follows:

Here is the probability density

A particle is described by the wave function as follows:

Here L is 2.0nm

The probability density of the particle at is as follows:

The probability density of the particle at is as follows:

These are the constant

Thus the probability of finding the particle within 1.0mm for the origin is 63.2%

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