Use the following equation statement to answer the question. The normalized wave functions for the infinite square-well potential are
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-The expectation value <x> for a particle in its first excited (n = 2) state in a box of length L is

Question

Use the following equation statement to answer the question. The normalized wave functions for the infinite square-well potential are
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-The expectation value <x> for a particle in its first excited (n = 2)state in a box of length L is
A)L 
B)3L/4 
C)L/2 
D)L/4 
E)L/8

Quizplus · Accepted Answer

The expectation value of x for the nth energy state is given by: = ∫ψ*n*(x) x ψn(x) dx from 0 to L For n=2, the wave function is ψ2(x) = sqrt(2/L)sin(2πx/L). Substituting this wave function and integrating, we get: = ∫[sqrt(2/L)sin(2πx/L)]^2 x dx from 0 to L = L/2 Therefore, the correct answer is C) L/2.

Use the Following Equation Statement to Answer the Question