Question

3. The ground state of the finite square well is $\phi_{E1}(x) = \sqrt{\frac{q}{qa+1}} \begin{cases} \frac{1}{z_0}e^{q(x+a)}, & x<-a\\cos(z_1x/a), & 0<x<a\\\frac{1}{z_0}e^{-q(x-a)}, & x>a\end{cases}$ Find the probability that the particle is found inside the well.

          3.
The ground state of the finite square well is
$\phi_{E1}(x) = \sqrt{\frac{q}{qa+1}} \begin{cases} \frac{1}{z_0}e^{q(x+a)}, & x<-a\\cos(z_1x/a), & 0<x<a\\\frac{1}{z_0}e^{-q(x-a)}, & x>a\end{cases}$
Find the probability that the particle is found inside the well.

3.
The ground state of the finite square well is
ϕE1(x) = √((q)/(qa+1))(1)/(z0)e^q(x+a), x<-a
cos(z1x/a), 0<x<a
(1)/(z0)e^-q(x-a), x>a
Find the probability that the particle is found inside the well.

Added by Patrick H.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Sarita Rana

Step 1

To find the probability, we need to normalize the wavefunction. The normalization condition is given by: ∫(|Ψ(x)|^2)dx = 1 For the given wavefunction, we have two regions: -a < x < 0 and 0 ≤ x ≤ a. We need to calculate the integral separately for each Show more…

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The ground state of the finite square well is Ïˆ(x) = âŽ§âŽªâŽ¨âŽªâŽ© âˆ’a cos(Ï€x/a), -a < x < 0 1 + b e^(-qx-a), 0 â‰¤ x â‰¤ a 0, otherwise Find the probability that the particle is found inside the well.