Question

E7C.15 Find $ \langle x \rangle $ when the wavefunction is $\psi(x) = \left(\frac{2}{L}\right)^{1/2}\sin\left(\frac{\pi x}{L}\right)$ for a particle confined between $x = 0$ and $x = L.$

Name: E7C.15 Find ⟨ x ⟩ when the wavefunction is ψ(x) = ((2)/(L))^1/2sin((π x)/(L)) for a particle confined between x = 0 and x = L.
Uploaded: 2023-09-13T18:44:16-08:00
Duration: 5 min 41 s
Channel: Adi S
Description: E7C.15 Find ⟨ x ⟩ when the wavefunction is ψ(x) = ((2)/(L))^1/2sin((π x)/(L)) for a particle confined between x = 0 and x = L.

          E7C.15 Find \( \langle x \rangle \) when the wavefunction is $\psi(x) = \left(\frac{2}{L}\right)^{1/2}\sin\left(\frac{\pi x}{L}\right)$ for a particle confined between $x = 0$ and $x = L.$

Added by Rebecca B.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Adi S

09/13/2023

Step 1

Step 1: Normalize the wavefunction To find the normalization constant, we need to integrate the square of the wavefunction over the entire range of x (from 0 to L) and set it equal to 1: ∫|ψ(x)|^2 dx = 1 ∫((2/L)^(1/2)sin(πx/L))^2 dx = 1 ∫(2/L)sin^2(πx/L) dx = Show more…

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