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 the ground state of an infinite square-well potential 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 the ground state of an infinite square-well potential is
A)L 
B)3L/4 
C)L/2 
D)L/4 
E)L/8

Quizplus · Accepted Answer

The expectation value of x can be calculated using the formula: = ∫(Ψ*(x)xΨ(x))dx from -L/2 to L/2 For the ground state, the wave function is Ψ(x) = sqrt(2/L)sin(πx/L) Substituting this in the formula, and after simplifying, we get the answer as = L/2. Therefore, the correct choice is C.

Use the Following Equation Statement to Answer the Question