2.2: Energy Function

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Nov 3, 2024
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- 2.1: Conservative Fields
- 2.3: Simple Example

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Of course the kinetic energy is $\frac{1}{2} m v^2$ , with $v=r$

$E=\frac{1}{2} m v^2+V(r)$

Actually, this form is not very convenient for quantum mechanics. We rather work with the so-called momentum variable $p=m v$ . Then the energy functional takes the form

$E=\frac{1}{2} \frac{p^2}{m}+V(r)$

The energy expressed in terms of $p$ and $r$ is often called the (classical) Hamiltonian, and will be shown to have a clear quantum analog.

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