10. A particle is represented by the following wave function: (x) = 0 = C(2x/L + 1) C(-2x/L + 1) = = 0 x <-L/2 -L/2 +L/2 (a) Use the normalization condition to find C. (b) Evaluate the probability to find the particle in an interval of width 0.010L at x = L/4 (that is, between x = 0.245L and x = 0.255L. (No integral is necessary for this calculation.) (c) Evaluate the probability to find the particle between x = 0 and x = +L/4. (d) Find the average value of x and the rms value of x: rms=√(2²) av

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10. A particle is represented by the following wave function:
(x) = 0
=
C(2x/L + 1)
C(-2x/L + 1)
=
= 0
x <-L/2
-L/2<x<0
0<x<+L/2
*> +L/2
(a) Use the normalization condition to find C. (b) Evaluate the probability to find the particle in an interval of width
0.010L at x = L/4 (that is, between x = 0.245L and x = 0.255L. (No integral is necessary for this calculation.) (c)
Evaluate the probability to find the particle between x = 0 and x=+L/4. (d) Find the average value of x and the rms
value of x: rms=√(2²) av
Transcribed Image Text:10. A particle is represented by the following wave function: (x) = 0 = C(2x/L + 1) C(-2x/L + 1) = = 0 x <-L/2 -L/2<x<0 0<x<+L/2 *> +L/2 (a) Use the normalization condition to find C. (b) Evaluate the probability to find the particle in an interval of width 0.010L at x = L/4 (that is, between x = 0.245L and x = 0.255L. (No integral is necessary for this calculation.) (c) Evaluate the probability to find the particle between x = 0 and x=+L/4. (d) Find the average value of x and the rms value of x: rms=√(2²) av
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