The Kronecker Delta Function Song

Walter F. Smith, Spring 2002




G†††††††††††††††††††† C††††††††††††† D†††††††††††††††††††††††† G

Leopold Kronecker said that God had


G†††††††††††††††††††† C†††††††††††††††††††††††††† D††††††††††††††††††† G

Made the integers but nothing in between.


†††††††††††† G††††††††††††††† C†††††††††††††††††† D††††††††††††††††††††††††††††††††† G

The study of transcen-dental numbers was mad!


†††† G†††††††††††††††† C†††††††††††††††††††††††††††† D†††††††††††††††††††††††††††††††† †††††††††††G††††††††††††††††

And the irrationals, he thought they were obscene!



†††††††††††† Em†††††††††††††††††††††††††† C†††††††††††††††††††††††† D†††††††††††††††† G

Although he was eccentric, old Leo was hero!


††††††††††† Em†††††††††††† C††††††††††† D†††††††††††††††††††††††††††††††††††† G

He studied elliptic functions, so they say.


††††††††††††††††† Em††††††††††††††††††††††††††† C††††††††††††††††††††† D††††††††††††††††††††††††††† G

But he did something else, and it equals one or zero--


Em†††††††††††††††††††††††††††††† C†††††††††††††††††††††††† D†††††††††††††††††††††††††††††† G

Itís the reason physicists remember him today!




†††††† G††††††††††††† †††† C†††††††††† D†††††††††††††††††††††††† G

Kronecker delta functions are such fun --


G†††††††††† †††††C††††††††††††††††††††††† D††††††††††† G

A little delta and a tiny m- n !


††††††††††††††† G††††††††††††††††††††††††††† C†††††††††††††††††††††† D††††††††††††††† G

If the subscripts are equal, the value is just one,

††††††††††††† G††††††††††††††††††† †††††††††C†††††††††††††††††††††††††††† D††††††††††††††††††††††††††††††† G††††††††††††††††

But zero if theyíre different, letís sing the song again!(2X)

†††††††††††††††††††††††††††† ††††††††††††† thatís enough, this is the end!(last time)



2002 Walter Fox Smith