Landau Energy Spectrum in the non-relativistic limit

[desperate_student]

Homework Statement

In the relativistic landau energy spectrum for a particle in a magnetic field, how does the m^2 term simplify down to p^2/2m in the non-relativistic limit?

Relevant Equations

Non-Relativistic: E=p^2/2m +w(n+1/2), n=0,1,2....
Relativistic: E= sqrt(p^2 +m^2+2mw(n+1/2)) n=0,1,2....

At non-relativistic limit, m>>p so let p=0
At non-relativistic limit m>>w,
So factorise out m^2 from the square root to get:
m*sqrt(1+2w(n+1/2)/m)
Taylor expansion identity for sqrt(1+x) for small x gives:
E=m+w(n+1/2) but it should equal E=p^2/2m +w(n+1/2), so how does m transform into p^2/2m?

 

[DrClaude]

At non-relativistic limit, m>>p so let p=0

If you set p=0, it should be obvious that you will not get an equation that depends on p. So try it again without doing that.