A particle is described by the wave function: Ψ(x)=b(a2-x2), for -a≤ x ≤ +a, and Ψ(x)=0 for -a ≥ x ≤ +a, where a and b are positive real constants. i) Using the normalization equation, find b in terms of a ii) What is the probability of finding the particle at x=+a/2 in the interval of width 0.010a? iii) What is the probability of finding the particle between x=+a/2 and x=+a?

A particle is described by the wave function: Ψ(x)=b(a2-x2), for -a≤ x ≤ +a, and Ψ(x)=0 for -a ≥ x ≤ +a, where a and b are positive real constants. i) Using the normalization equation, find b in terms of a ii) What is the probability of finding the particle at x=+a/2 in the interval of width 0.010a? iii) What is the probability of finding the particle between x=+a/2 and x=+a?

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Question

A particle is described by the wave function:

Ψ(x)=b(a²-x²), for -a≤ x ≤ +a,

and Ψ(x)=0 for -a ≥ x ≤ +a,

where a and b are positive real constants.

i) Using the normalization equation, find b in terms of a

ii) What is the probability of finding the particle at x=+a/2 in the interval of width 0.010a?

iii) What is the probability of finding the particle between x=+a/2 and x=+a?

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