Probability that the particle will be found? Part A part B Please work out the s

Question

Probability that the particle will be found?

Part A

part B

Please work out the solution step by step

The wave function of a particle is psi (x) = {b/(1 + x2) - 1 mm x 0 mm c(1 + x)2 0 mm x 1 mm} and zero elsewhere. You will learn in the textbook that the wave function must be a continuous function. Assuming that to be the case, what can you conclude about the relationship between b and c? b c What is the probability that the particle will be found to the right of the origin? Express your answer using two significant figures.

Explanation / Answer

a) so psi(0) = psi(0)

b/1 = c*1

so b = c

b) P anywhere = integral of b/(1+x^2) from -1 to 0 + integral of b*(1+x^2) from 0 to 1

= pi b/4 + 4 b/3 = 1

b ( pi/4 + 4/3) = 1

b = 1/( pi/4 + 4/3)

P(x>0) = integral of b*(1+x^2) from 0 to 1 = 4 b/3 = 4/3* 1/( pi/4 + 4/3)= 0.63 = 63%

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.