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The differential rate equation for an elementary reaction using product notation is:

Where:

  • is the rate of change of reactant concentration with respect to time.
  • k is the rate constant of the reaction.
  • represents the concentration of each reactant raised to the power of its stoichiometric coefficient and multiplied together.

The second-order differential equation for a serial CLR circuit can be derived from Kirchhoff's voltage law and Ohm's law. It's given by:

Where:

This equation describes the behavior of the charge on the capacitor in response to a time-varying voltage source.


The time-dependent Schrödinger equation is given by:

Here:

This equation describes how the quantum state of a physical system changes with time.


The lateral shift of light passing through a glass slab is given by:

where:

Combining this with the Snell's law, the full expression for the lateral shift becomes:

The cumulative lateral shift through a combination of glass slabs can be computed with the principle of superposition of individual lateral shifts through each slab. This assumes the angles remain small enough that higher-order effects can be neglected.

The total lateral shift through n slabs is given by:

where:

  • ti is the thickness of the i-th slab.
  • θi is the angle of incidence at the i-th slab.
  • θi+1 is the angle of refraction for the i-th slab.

Combining this with the Snell's law, the full expression for the total lateral shift through n slabs becomes: