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GR8677 #49
Problem
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Quantum Mechanics$\Rightarrow$}Schrodinger Equation

Recall the Time-independent Schrodinger Equation,

$H\psi=E\psi\Rightarrow -\frac{\hbar^2}{2m}\psi '' + V(x) \psi = E\psi,
$

where $H=-\frac{\hbar^2}{2m}\psi '' + V(x) \psi = E\psi$.

The classical Hamiltonian is $H=\frac{p^2}{2m} + V(x)$, where one sees the only difference is $p \rightarrow \frac{\hbar}{i}\frac{d}{dx}$. From the classical Hami, one can directly reach the Hami operator in the TISE via substituting a differential operator for momentum, as in choice (B).

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