(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Show that variation principle (parameters ci) leads to equations

[tex]

\sum\limits_{i = 1}^n {\left\langle i \right|H\left| j \right\rangle c_j = Ec_i {\rm{ where }}} \left\langle j \right|H\left| i \right\rangle = \int {d\textbf{r}^3 \chi _j^* \left( \textbf{r} \right)\left( {H\chi _i \left( \textbf{r} \right)} \right)}

[/tex]

2. Relevant equations

I've got [tex]

\psi \left( \textbf{r} \right) = \sum\limits_{i = 1}^n {c_i \chi _i \left( \textbf{r} \right)}

[/tex]

, but

3. The attempt at a solution

I'm confused about what's being asked, and what the expected result means. Indices as kets and bras? If they're different vectors within the Hilbert space, won't they be orthonormal implying all i not equal j would be zero? I have a nagging feeling I'm either confused by notation or overlooking something basic.

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: QM Variation Method

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