Why is the expectation value of the energy associated with the 1-D "particle-in-a-box" the same as the eigen value of the Hamilt
onian associated with the 1-D "particle-in-a-box" wave function?
1 answer:
Answer: The average potential energy of the PIB is 0 irrespective of the wave function.
Explanation:
⟨H⟩=⟨KE⟩+⟨V⟩
the nn quantum number
⟨KE⟩=(π^2 ℏ^2)/(2mL^2 )
the average kinetic energy of the wavefunction is dependent on
⟨V⟩=∫sin(kx)0sin(kx)dx=0
The average potential energy of the PIB is 0 irrespective of the wave function.
⟨H⟩=⟨KE⟩=(π^2 ℏ^2)/(2mL^2 )
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