- #1

warhammer

- 158

- 31

- Homework Statement
- Consider two states of a particle given by the wave functions

ψ1(x) = √re-|r|x and ψ2(x) = -√re-|r|x

The probability of finding the particle in the range -1/r < x < 1/r is p1 in the first state and p2 in the second state. Which of the following is appropriate?

(a) p1 = p2

(b) p1 = - p2

(c) p1 < p2

(d) p1 > p2

- Relevant Equations
- Integration {ψ(x)}{ψ(x)*} from -∞ to ∞=1

(* denotes conjugate)

I calculated the complex conjugate of both the given wavefunctions. For ψ1: ∫re^((-2)mod(r)x)dx=1 with upper limit ∞ & lower limit -∞. I replaced the upper and lower limit after breaking down the function inside integration as follows- r*∫e^(2rx)dx from -1/r to 0 and r*e∫e^(-2rx)dx from 0 to 1/r. The answer was 1-1/e^2 which equals 0.86.

I repeated the above steps for ψ2 and similarly obtained 0.86. However, I am somewhat not sure if I have proceeded correctly.

I repeated the above steps for ψ2 and similarly obtained 0.86. However, I am somewhat not sure if I have proceeded correctly.