In physics, it is often necessary to make certain assumptions to simplify a complicated problem to make it tractable. We might make assumptions about symmetry, say that a certain small value is essentially zero, talk about what happens when a certain value is infinity, or any of a host of other simplifications that would make a mathematician cringe and make a layman wonder how he can take our results seriously.
We often make light of this tendency by talking about spherical cows. Obviously, a spherical cow is a pretty ridiculous picture:
A cow only a physicist could love.
However, in certain situations, estimating the cow as a sphere with a characteristic radius might not be as ridiculous as it seems. For example, if the car were flying through the air (or standing in a strong wind, if flying spherical cows are too much for you to accept), the air resistance on a sphere the size of a cow would be a pretty accurate approximation.
But of course, the spherical cow is most useful as a metaphor for the approximation techniques we do use. So what are these simplificaton techniques? Read on to find out.
The First Excited State 