Recent content by LesterTU

Homework Statement We are given a Lorentz four-vector in "isospin space" with three components ##\vec v^{\mu} = (v^{\mu}_1, v^{\mu}_2, v^{\mu}_3)## and want to express the covariant derivative $$D^{\mu} = {\partial}^{\mu} - ig\frac {\vec \tau} {2}\cdot \vec v^{\mu}$$ explicitly in ##2\times 2##...

Thank you very much! They introduced the concept of effective mass in the lectures by stating the definition and giving us an intuitive feel for what it is based on the curvature of the bands, but they never told us how to actually apply it in practice or showed a concrete example, yet this...

So at ##\mathbf k = 0##, we get $$\left( m^* \right)_{xx} = \frac{\hbar ^2}{Aa^2} \ \ \ \ \ \ \left( m^* \right)_{yy} = \frac{\hbar ^2}{Bb^2} \ \ \ \ \ \ \left( m^* \right)_{zz} = \frac{\hbar ^2}{Cc^2}$$ Does this answer the question "What is the value of the effective mass tensor ## \left(...

So you take the second derivative of ##E(\mathbf k)## with respect to all nine combinations of ##i, j##, and add them together? The cross terms would vanish, and we are left with $$ \frac {\partial^2 E(\mathbf k)} {\partial k_x \partial k_x} = Aa^2cos(k_xa)$$ and similarly for yy and zz. Thus...

Homework Statement The energy-band dispersion for a 3D crystal is given by $$E(\mathbf k) = E_0 - Acos(k_xa) - Bcos(k_yb) - Ccos(k_zc)$$ What is the value of the effective mass tensor at ## \mathbf k = 0 ##? Homework Equations The effective mass tensor is given by $$ \left( \frac{1}{m^*}...

Thanks! I guess the friction applies in this case but for some reason because of its direct relationship with the normal force I didn't consider it. It makes a lot of sense though now that I think about it

Homework Statement A 30-kg child is on a rotor ride at a carnival. The radius of the rotor is 3 m and it completes 0.4 revolutions in one second. The coefficient of static friction is 0.6. What is the magnitude of the child's apparent weight? Homework Equations ΣFx : FN = mv2/r ΣFy : Ff = Fg...