Prob-Current2011

# Prob-Current2011 - Physical Chemistry Course Number: C362...

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Unformatted text preview: Physical Chemistry Course Number: C362 16 Additional reading: Probability Current 1. Consider the time-dependent Schrodinger Equation and its complex conju- gate: h t ( x, t ) = H ( x, t ) = h 2 2 m 2 x 2 + V ( x, t ) (16.10) h t ( x, t ) = H ( x, t ) = h 2 2 m 2 x 2 + V ( x, t ) (16.11) 2. Multiply Eq. ( 16.10 ) by ( x, t ) , and Eq. ( 16.11 ) by ( x, t ) : ( x, t ) h t ( x, t ) = ( x, t ) H ( x, t ) = ( x, t ) h 2 2 m 2 x 2 + V ( x, t ) (16.12) ( x, t ) h t ( x, t ) = ( x, t ) H ( x, t ) = ( x, t ) h 2 2 m 2 x 2 + V ( x, t ) (16.13) 3. Subtract the two equations to obtain (see that the terms involving V cancels out) h t [ ( x, t ) ( x, t )] = h 2 2 m ( x, t ) 2 x...
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## Prob-Current2011 - Physical Chemistry Course Number: C362...

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