- #1

- 13

- 1

Given the relativistic equation for energy E

I want to find the non-relativistic approximation for kinetic energy in non-relativistic terms,

K

I start off with subtracting the rest energy

E

from the above equation.

So K = E - E

and assume that c is very large.

I've messed around for hours on the algebra and I need help.

I want to show that K ≈ K

I am doing this using a linear approximation. I've written the energy as E = E

And using the function f(x)=√1+x about x = 0

I've derived the linearization as L(x) = 1 + x/2

But I am struggling with relating to the equations above to show that K ≈ K

^{2}= (pc)^{2}+ (mc^{2})^{2}I want to find the non-relativistic approximation for kinetic energy in non-relativistic terms,

K

_{nr}= p^{2}/2mI start off with subtracting the rest energy

E

_{0}=mc_{2}from the above equation.

So K = E - E

_{0}and assume that c is very large.

I've messed around for hours on the algebra and I need help.

I want to show that K ≈ K

_{nr}I am doing this using a linear approximation. I've written the energy as E = E

_{0}√1+xAnd using the function f(x)=√1+x about x = 0

I've derived the linearization as L(x) = 1 + x/2

But I am struggling with relating to the equations above to show that K ≈ K

_{nr}
Last edited: