{tag=Spring-mass system}

Both are <harmonic oscillators>.

In the <LC circuit>:
* the current current may be seen as the velocity and containing the <kinetic energy>
* the charge stored in the capacitor as the <potential energy>

You can kickstart motion in either of those systems in two ways:
* charge the capacitor, i.e. pull the string, and then let it go, i.e. close the circuit. This is the simpler one to realise. Shown concretely at: <video LC circuit dampened oscillations on an oscilloscope by Queuerious Guy (2014)>
* give speed to the mass, i.e. make a current pass through the inductor


An LC circuit is analogous to a spring-mass system

{c}

We select for the general <equation Schrodinger equation>:
* $\vv{x} = x$, the linear <cartesian coordinate> in the x direction
* $\hat{H} = -\frac{\hbar^2}{2m}\pdv{^2}{x^2} + V(x, t)$, which analogous to the sum of <kinetic energy>[kinetic] and <potential energy> in <classical mechanics>
giving the full explicit <partial differential equation>:
$$
i\hbar\pdv{\psi(x, t)}{t} = \left[ -\frac{\hbar^2}{2m}\pdv{^2}{x^2} + V(x, t) \right]\psi(x, t)
$$
{title=<Schrödinger equation> for a one dimensional particle}

The corresponding <time-independent Schrödinger equation> for this equation is:
$$
\left[-\frac{\hbar^2}{2m} \pdv{^2}{x^2} + V(x)\right]\psi(x) = E \psi(x)
$$
{title=<time-independent Schrödinger equation> for a one dimensional particle}


Ciro Santilli @cirosantilli 37

 Incoming links: Kinetic energy