GREPhysics.NET: GR8677 #49

GR8677 #49

Problem

GREPhysics.NET Official Solution

Alternate Solutions

Quantum Mechanics $\Rightarrow$ }Schrodinger Equation

Recall the Time-independent Schrodinger Equation,

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

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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LaTeX syntax supported through dollar sign wrappers $, ex., $\alpha^2_0$ produces $\alpha^2_0$ .
type this...	to get...
$\int_0^\infty$	$\int_0^\infty$
$\partial$	$\partial$
$\Rightarrow$	$\Rightarrow$
$\ddot{x},\dot{x}$	$\ddot{x},\dot{x}$
$\sqrt{z}$	$\sqrt{z}$
$\langle my \rangle$	$\langle my \rangle$
$\left( abacadabra \right)_{me}$	$\left( abacadabra \right)_{me}$
$\vec{E}$	$\vec{E}$
$\frac{a}{b}$	$\frac{a}{b}$

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