Calculating Energy in a Quantum Chemistry System

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The discussion focuses on calculating the second lowest energy measurement in a quantum chemistry system defined by the wave function Psi(x) = Ax(b/2 - x) for 0 < x < b/2 and Psi(x) = 0 for b/2 < x < b. The user is uncertain whether to treat the system as a box of width b or b/2 for energy state calculations. They aim to find the probability of measuring energy E2 by expanding the initial state in terms of the energy operator's eigenfunctions, specifically using the sine function derived for a box of width b. The key challenge is determining the correct width for the box and ensuring the proper incorporation of wave equations. Clarification on these points is sought to confirm the approach is valid.
Knight
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There is an initial state Psi(x) =Ax(b/2 - x) when 0< x <b/2 and Psi(x) = 0 when b/2 < x <b

I have to find the second lowest value possibly be obtained in a measurement of the energy.

Should I treat this as a box with width b and possible energy states E=n^2*h^2/8mb^2 ? Or should I use the width b/2 ?

Could someone please help me?
 
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How are you going to incorporate the wave equations?
 
Let me explain this problem better.
What I have to do is calculate the propability that the measured energy from this system is E2
O.K. So I have to find the Fourier coefficients, when I expand the initial state I mentioned above from 0 to b/2 in the eigenfunctions of the energy operator, or sqrt(2/b)*sin(n*pi*x/b). I know these eigenfunctions are derived from x=0 to x=b but Psi(x) =Ax(b/2 - x) is when 0< x <b/2
I am doing this the correct way or am I way off?
 
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