Incoming links: Potential energy
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
We select for the general Equation "Schrodinger equation":giving the full explicit partial differential equation:
- , the linear cartesian coordinate in the x direction
- , which analogous to the sum of kinetic and potential energy in classical mechanics
Equation 1.
Schrödinger equation for a one dimensional particle
. The corresponding time-independent Schrödinger equation for this equation is:
Equation 2.
time-independent Schrödinger equation for a one dimensional particle
. - why the square: physics.stackexchange.com/questions/535/why-does-kinetic-energy-increase-quadratically-not-linearly-with-speed on Physics Stack Exchange. Ron Maimon's answer is great, as it relies only on the following staring points:He also offers a symmetry argument considering the case of potential energy.
- why the half: physics.stackexchange.com/questions/27847/why-is-there-a-frac-1-2-in-frac-1-2-mv2 on Physics Stack Exchange